Distance, Speed Distance, Speed NotesNotes

Distance, SpeedDistance, Speed

There are 4 ways to quantify motion:There are 4 ways to quantify motion:

How far (distance/displacement)How far (distance/displacement) How fast (speed/velocity)How fast (speed/velocity) DirectionDirection AccelerationAcceleration

DistanceDistance

Distance of motion is the measured Distance of motion is the measured movement of one object relative to movement of one object relative to another. The object we compare to is another. The object we compare to is called the reference object, and is usually called the reference object, and is usually the Earththe Earth

We should consider the reference object We should consider the reference object stationary. When an object moves stationary. When an object moves relative to another object, it will have relative to another object, it will have traveled some distancetraveled some distance

DistanceDistance

Distance is a Distance is a scalarscalar quantity (magnitude quantity (magnitude only, no direction)only, no direction)

DisplacementDisplacement

Displacement is the change in position of Displacement is the change in position of an object, or the length of a straight line an object, or the length of a straight line from its initial position to its final position. from its initial position to its final position. When an object moves relative to When an object moves relative to another, it will not necessarily have another, it will not necessarily have undergone any displacement.undergone any displacement.

DisplacementDisplacement

Displacement is a Displacement is a vectorvector quantity quantity (magnitude and direction are described)(magnitude and direction are described)

ΔΔx = xx = xff - x - xii

SpeedSpeed

Speed is described as the rate of Speed is described as the rate of movementmovement

Average speed = distance / timeAverage speed = distance / time

Example: A race car goes around a 1 mile Example: A race car goes around a 1 mile oval track in 15 seconds. Its average oval track in 15 seconds. Its average speed would be 240 mi/hrspeed would be 240 mi/hr

SpeedSpeed

Speed is a scalar quantitySpeed is a scalar quantity

Traditional Units:Traditional Units: Metric units: m/sMetric units: m/s English units: mi/hr, ft/sEnglish units: mi/hr, ft/s

VelocityVelocity

Velocity is described as the rate of Velocity is described as the rate of displacementdisplacement

Average velocity = displacement / timeAverage velocity = displacement / time

Example: A race car goes around a 1 mile Example: A race car goes around a 1 mile oval track in 15 seconds. Its average oval track in 15 seconds. Its average velocity would be 0 mi/hr.velocity would be 0 mi/hr.

VelocityVelocity

Velocity is a vector quantity. It has the Velocity is a vector quantity. It has the same units as speed, but direction should same units as speed, but direction should be signified.be signified.

VelocityVelocity

If a graph is drawn with displacement on If a graph is drawn with displacement on the y-axis and time on the x-axis, the the y-axis and time on the x-axis, the slope of that graph would show the slope of that graph would show the average velocityaverage velocity

Slope = rise/run = Slope = rise/run = ΔΔy / y / ΔΔx = x = ΔΔx / x / ΔΔtt

= = ΔΔd / d / ΔΔt = v t = v aveave

VelocityVelocity

Therefore, a steep positive slope Therefore, a steep positive slope corresponds to a large average velocity, corresponds to a large average velocity, a steep negative slope would correspond a steep negative slope would correspond to a large negative average velocity, a to a large negative average velocity, a flatter positive slope would correspond to flatter positive slope would correspond to a smaller positive average velocity, etc.a smaller positive average velocity, etc.

VelocityVelocity

vvave ave = = ΔΔx / x / ΔΔt = t = ΔΔd / d / ΔΔtt

= (x= (xff – x – xii) / (t) / (tff – t – tii) )

Instantaneous Velocity: Velocity at a given Instantaneous Velocity: Velocity at a given instant in time. This cannot be calculated instant in time. This cannot be calculated without knowing the constant without knowing the constant acceleration or using calculus.acceleration or using calculus.