Representing motion

The speed of an object can be calculated if the distance travelled and the time taken is known. The faster an object moves, the steeper is the line representing it on a distance-time graph. The speed is equal to the gradient of the line on a distance-time graph.

The velocity of an object is its speed in a particular direction. The acceleration of an object is equal to the gradient of the line on a velocity-time graph. The distance travelled is equal to the area under a velocity-time graph.

1. Speed, distance and time 2. Distance-time graphs 3. Velocity-time graphs 4. Acceleration 5. Distance-time graphs (Higher Tier) 6. Velocity-time graphs (Higher Tier)

Speed, distance and time

You should recall from your Key Stage 3 studies how to calculate the speed of an object from the distance travelled and the time taken.

The equationWhen an object moves in a straight line at a steady speed, you can calculate its speed if you know how far it travels and how long it takes. This equation shows the relationship between speed, distance travelled and time taken:

For example, a car travels 300m in 20s.

Its speed is 300 ÷ 20 = 15m/s.

Check your understanding of this topic by having a go at this activity.

Distance-time graphs

You should be able to draw and explain distance-time graphs for objects moving at steady speeds or standing still.

Background informationThe vertical axis of a distance-time graph is the distance travelled from the start, and the horizontal axis is the time from the start.

Features of the graphsWhen an object is stationary, the line on the graph is horizontal.

When an object is moving at a steady speed, the line on the graph is straight, but sloped.

The diagram shows some typical lines on a distance-time graph.

Note that the steeper the line, the greater the speed of the object. The blue line is steeper than the red line because it represents an object moving faster than the one represented by the red line.

The red lines on the graph represent a typical journey where an object returns to the start again. Notice that the line representing the return journey slopes downwards.

Velocity-time graphs

You should be able to explain velocity-time graphs for objects moving with a constant velocity or a constant acceleration.

Background informationThe velocity of an object is its speed in a particular direction. This means that two cars travelling at the same speed, but in opposite directions, have different velocities.

The vertical axis of a velocity-time graph is the velocity of the object and the horizontal axis is the time from the start.

Features of the graphsWhen an object is moving with a constant velocity, the line on the graph is horizontal. When an object is moving with a constant acceleration, the line on the graph is straight, but sloped. The diagram shows some typical lines on a velocity-time graph.

The steeper the line, the greater the acceleration of the object. The blue line is steeper than the red line because it represents an object with a greater acceleration than the one represented by the red line.

Notice that a line sloping downwards (with a negative gradient) represents an object with a constant deceleration (slowing down).

Acceleration

You should be able to calculate the acceleration of an object from its change in velocity and the time taken.

The equationWhen an object moves in a straight line with a constant acceleration, you can calculate its acceleration if you know how much its velocity changes and how long this takes. This equation shows the relationship between acceleration, change in velocity and time taken:

For example, a car accelerates in 5s from 25m/s to 35m/s.

Its velocity changes by 35 – 25 = 10 m/s.

So, its acceleration is 10 ÷ 5 = 2m/s2.

Distance-time graphs (Higher Tier)

You should be able to calculate gradients on distance-time graphs.

BackgroundTo calculate the gradient of the line on a graph, divide the change in the vertical axis by the change in the horizontal axis.

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Distance-time graphsThe gradient of a line on a distance-time graph represents the speed of the object. Study this distance-time graph.

What is the speed represented by the blue line?

The object travels 10m in 2s. Its speed is 10 ÷ 2 = 5m/s.

Check your understanding of this by having a go at this activity.

Velocity-time graphs (Higher Tier)

You should be able to calculate gradients of velocity-time graphs and the areas under the graphs.

The gradientThe gradient of a line on a velocity-time graph represents the acceleration of the object. Study this velocity-time graph.

What is the acceleration represented by the sloping line?The object increases its velocity from 0m/s to 8m/s in 4s. Its acceleration is 8 ÷ 4 = 2m/s2.

The areaThe area under the curve in a velocity-time graph represents the distance travelled. To find the the distance travelled in the graph above we need to find the area of the light blue triangle and the dark blue square

Step 1 - Area of light blue triangleThe width of the triangle is 4 seconds and the height is 8 metres per second. To find area you use the equation:area of triangle = 1/2 x base x heightso the area of the light blue triangle is 1/2 x 8 x 4 = 16m.

Step 2 - Area of dark blue rectangleThe width of the rectangle is 6 seconds and the height is 8 metres per second so the area is 8 x 6 = 48m.

Step 3 - Area under the whole graphThe area of the light blue triangle plus the area of the dark blue rectangle is:16 + 48 = 64m.This is the total area under the distance time graph and this area represents the distance covered.

To summarise:

the gradient of a velocity time graph represents the acceleration the area under a distance time graph represents the distance covered

Check your understanding of this by having a go at the following activity.

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Now try a Test Bite (Foundation)

Test Bite (Higher)

Representing motion

1. A car travels 100m in 5s. What is its average speed?

a) 500m/s

b) 20m/s

c) 0.05m/s

2. What does a horizontal line on a distance-time graph represent?

a) Constant acceleration

b) Constant speed

c) Stationary object

3. Which line on the graph below represents the greatest speed?

a)

b)

c)

4. What does a horizontal line on a velocity-time graph represent?

a) Constant acceleration

b) Constant velocity

c) Stationary object

5. Which line on the graph below represents the greatest acceleration?

a)

b)

c)

6. A car accelerates from rest to 30m/s in 15s. What is its acceleration?

a) 45m/s2

b) 450m/s2

c) 2m/s2

Representing motion

1. A car travels 100m in 5s. What is its average speed?

a) 500m/s

b) 20m/s

c) 0.05m/s

2. What does a horizontal line on a distance-time graph represent?

a) Constant acceleration

b) Constant speed

c) Stationary object

3. Which line on the graph below represents the greatest speed?

a) A

b) B

c) C

4. What does a horizontal line on a velocity-time graph represent?

a) Constant acceleration

b) Constant velocity

c) Stationary object

5. Which line on the graph below represents the greatest acceleration?

a) A

b) B

c) C

6. A car accelerates from rest to 30m/s in 15s. What is its acceleration?

a) 45m/s2

b) 450m/s2

c) 2m/s2

7. What does the gradient on a distance-time graph represent?

a) Distance travelled

b) Speed

c) Acceleration

8. What does the gradient on a velocity-time graph represent?

a) Distance travelled

b) Speed

c) Acceleration

9. What does the area under a velocity-time graph represent?

a) Distance travelled

b) Speed

c) Acceleration

Force, mass and accelerationIf the forces acting on an object are balanced, a stationary object remains stationary, and a moving object keeps moving at the same speed and in the same direction.

If the forces acting on an object are unbalanced, a stationary object begins to accelerate in the direction of the force, and a moving object speeds up, slows down or changes direction.

Acceleration depends on the force applied to an object and the mass of the object.

1. Balanced and unbalanced forces 2. Forces and acceleration 3. Forces and acceleration (Higher Tier) 4. Questions and answers

Balanced and unbalanced forces

You should be able to use the idea of balanced and unbalanced forces to determine the movement of an object.

Balanced forcesWhen all the forces acting on an object cancel out, we say that they are balanced. If the forces are balanced:

A stationary object remains stationary. A moving object keeps on moving at the same speed in the same direction.

For example, a book resting on a table has balanced forces. Its weight acting downwards is balanced by the upward force on the book provided by the table. In the diagram of the weightlifter, the forces on the bar are balanced, so it does not move.

The longer the arrow, the bigger the force. In this diagram, the arrows are the same length, so we know they are the same size.

Unbalanced forcesWhen all the forces acting on an object do not cancel out, we say they are unbalanced. If the forces are unbalanced:

A stationary object begins to move in the direction of the unbalanced force. A moving object speeds up, slows down or changes direction depending on the

direction of the unbalanced force.

In this diagram of the weightlifter, the forces on the bar are unbalanced. The upwards force is bigger than the downwards force, so the bar moves upwards.

In this diagram of the weightlifter, the forces on the bar are also unbalanced. The upwards force is smaller than the downwards force, so the bar moves downwards.

Forces and acceleration

You should know that unbalanced forces cause objects to accelerate, and understand the factors that affect the size of the acceleration.

Size of the forceAn object will accelerate in the direction of an unbalanced force. The bigger the force, the greater the acceleration. Click on the animation (below) to double the force applied to the trolley, and see what happens.

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Doubling the size of the unbalanced force doubles the acceleration.

The massAn object will accelerate in the direction of an unbalanced force. The bigger the mass of the object, the smaller the acceleration. Click on the animation below to increase the mass on the trolley, and see what happens.

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Doubling the mass halves the acceleration.

Forces and acceleration (Higher Tier)

You should know the equation that shows the relationship between force, mass and acceleration, and be able to use it.

The equation

You should see that 1N is the force needed to give 1kg an acceleration of 1m/s2.

For example, the force needed to accelerate a 10kg mass by 5m/s2 is 10 x 5 = 50N.The same force could accelerate a 1kg mass by 50m/s2 or a 100kg mass by 0.5m/s2.

Example

A truck has a mass of 2,000kg.The driving force created by the engine is 3,000 newtons.Calculate the acceleration caused by this unbalanced force.

Answer

1. Write down and rearrange the equation. force = mass x acceleration

2. Rearrange the equation. acceleration = force/mass

3. Put in the values. acceleration = 3,000N/2,000kg

4. Work out the answer and write it down. acceleration = 1.5m/s2

Check your understanding of this section by having a go at the activity.

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Questions and answers

Here are four typical forces on which you could be asked questions:

1. Air resistance (drag)When an object moves through the air, the force of air resistance acts in the opposite direction to the motion. Air resistance depends on the shape of the object and its speed.

2. Contact forceThis happens when two objects are pushed together. They exert equal and opposite forces on each other. The contact force from the ground pushes up on your feet as you push down to walk forwards.

3. FrictionThis is the force that resists movement between two surfaces, which are in contact.

4. GravityThis is the force that pulls objects towards the Earth. We call the force of gravity on an object its weight. The Earth pulls with a force of about 10 newtons on every kilogram of mass.

Sample questionsQuestion 1Look at the animation of the parachutist falling at a steady speed. Name the forces acting on the parachutist and state how they are acting.

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Answer 1There are just two forces acting on the parachutist. Gravity (weight) pulls the parachutist down. Air resistance (drag) pushes up on the canopy of the parachute.

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Question 2Look at the animation of the car moving at a steady speed. Name the forces acting on the car and state how they are acting.

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Answer 2There are several forces acting on the car. Gravity pulls down on the car. The contact force from the road pushes up on the wheels. The driving force from the engine pushes the car along. There is friction between the road and the tyres. There is friction in the wheel bearings. Air resistance acts on the front of the car.

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Now try a Test Bite (Foundation)

Test Bite (Higher)

Force, mass and acceleration

1. What happens to a moving object if the forces on it are balanced?

a) It stops.

b) It keeps moving.

c) It changes direction.

2. What happens to a moving object if the forces on it are unbalanced?

a) It speeds up in the direction of the unbalanced force.

b) It slows down in the direction of the unbalanced force.

c) It moves towards the unbalanced force.

3. What is the unit of force?

a) The newton (N)

b) The Newton (n)

c) The kilogram (kg)

4. If we double the force applied to an object, what happens to its acceleration?

a) It stays the same.

b) It doubles.

c) It halves.

5. The same force is applied to three balls. Which one will experience the greatest acceleration?

a) The 4kg ball.

b) The 2kg ball.

c) The 1kg ball.

Force, mass and acceleration

1. What happens to a moving object if the forces on it are balanced?

a) It stops.

b) It keeps moving.

c) It changes direction.

2. What happens to a moving object if the forces on it are unbalanced?

a) It speeds up in the direction of the unbalanced force.

b) It slows down in the direction of the unbalanced force.

c) It moves towards the unbalanced force.

3. What is the unit of force?

a) The newton (N)

b) The Newton (n)

c) The kilogram (kg)

4. If we double the force applied to an object, what happens to its acceleration?

a) It stays the same.

b) It doubles.

c) It halves.

5. The same force is applied to three balls. Which one will experience the greatest acceleration?

a) The 4kg ball.

b) The 2kg ball.

c) The 1kg ball.

6. What force is needed to give an acceleration of 2m/s2 to a 4kg box?

a) 2N

b) 6N

c) 8N

Friction and non-uniform motion

A falling object accelerates because of the force of gravity, but as it speeds up, the frictional forces on it increase. Eventually, the gravitational force is balanced by the frictional forces and the object falls at a constant speed, called the terminal velocity.

The distance travelled by a car between the time it takes for its driver to start reacting to a hazard and the car stopping depends on two things: the thinking distance and the braking distance. Several factors influence the thinking distance and the braking distance, and can increase the overall stopping distance.

1. Falling objects 2. Stopping distances 3. Safety in collisions (Higher Tier)

Falling objects

You should be able to describe the forces affecting a falling object at different stages of its fall.

OutlineWhen an object is dropped, we can identify three stages before it hits the ground:

At the start, the force of gravity pulls the object down towards the Earth, and it accelerates downwards.

As it gains speed, frictional forces on the object increase and oppose the downwards movement.

Eventually, the force of gravity acting on the object is balanced by the frictional forces. The object reaches a steady speed called the terminal velocity.

Check your understanding of this by studying the animation of a parachutist.

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Terminal velocityWhat happens if you drop a feather and a coin together? The feather and the coin have roughly the same surface area, so when they begin to fall they have about the same drag.

As the feather falls, its drag increases until it soon balances the weight of the feather. The feather now falls at its terminal velocity. But the coin is much heavier, so it has to travel quite fast before drag is large enough to balance its weight. In fact, it probably hits the ground before it reaches its terminal velocity.

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On the moonAn astronaut on the moon carried out a famous experiment. He dropped a hammer and a feather at the same time and found that they landed together. The moon's gravity is too weak for it to hold onto an atmosphere, so there is no air resistance. When the hammer and feather were dropped they fell together with the same acceleration.

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Stopping distances

You should know some of the factors affecting the stopping distance of a car.

Thinking distanceIt takes a certain amount of time for a driver to react to a hazard and to start applying the brakes. During this time, the car is still moving. The faster the car is travelling, the greater this thinking distance will be.

The thinking distance will also increase if the driver's reactions are slower because the driver is:

Under the influence of alcohol. Under the influence of drugs. Tired

Braking distanceThe braking distance is the distance the car travels from where the brakes are first applied to where the car stops. If the braking force is too great, the tyres may not grip the road sufficiently and the car may skid. The faster the car is travelling, the greater the braking distance will be.

The braking distance will also increase if:

The brakes or tyres are worn. The weather conditions are poor, such as icy or wet roads. The car is more heavily laden, for example with passengers and luggage.

Stopping distanceThe stopping distance is the thinking distance added to the braking distance. The graph

shows some typical stopping distances.

Safety in collisions (Higher Tier)

You might need to know about seat belts and crumple zones (check the requirements of your examination board).

BackgroundRecall the equation: force = mass × acceleration.

Your body has a certain mass, so the greater the acceleration or deceleration, the greater the force applied to it. When there is a car crash, the car and its contents decelerate rapidly. They experience great forces, which can cause injury. If the deceleration is reduced, the forces are reduced too. Seat belts and crumple zones are designed to reduce the deceleration if there is a collision.

Seat beltsSeat belts stop you tumbling around inside the car if there is a collision. However, they are designed to stretch a bit in a collision. This reduces the deceleration, but the seat belts must be replaced after an accident.

Crumple zonesModern cars are designed with a tough passenger cabin, surrounded by sections that are designed to crush and buckle in a collision. These sections are called crumple zones. During a collision, these sections absorb large amounts of kinetic energy as they bend and crumple, and they reduce the deceleration. The diagram shows a crumple zone in a car door before and after a collision.

Test Bite

Friction and non-uniform motion

1. In which direction does friction act?

a) In the same direction as the direction of movement.

b) In the opposite direction to the direction of movement.

c) At 90 degrees to the direction of movement.

2. Which force causes objects to fall?

a) Gravity

b) Kinetic energy

c) Friction

3. What can we say about the forces acting on an object at terminal velocity?

a) They are always very big.

b) They are unbalanced.

c) They are balanced.

4. Which of the following can increase the thinking distance for a moving car?

a) Worn brakes

b) A heavy load in the boot.

c) A tired driver.

5. Which of the following can increase the braking distance for a moving car?

a) Driving more slowly.

b) Icy roads

c) A driver who has drunk a pint of lager.