Speed vs.VelocitySpeed vs.Velocity

Speed (s)Speed (s) is the distance an object travels is the distance an object travels per unit of time (rate).per unit of time (rate).

Velocity (v)Velocity (v) describes the speed and describes the speed and direction of a moving object.direction of a moving object.

VelocityVelocity

Objects undergoing motion will either have Objects undergoing motion will either have a constant or changing velocitya constant or changing velocity

constant velocity constant velocity = not speeding up or = not speeding up or slowing down.slowing down.

changing velocity changing velocity = speeding up or slowing = speeding up or slowing down.down.

Constant / Zero Velocity Constant / Zero Velocity

Distance (m)Distance (m)

Time (s)Time (s)

Constant velocityConstant velocity

Zero VelocityZero Velocity

Changing VelocityChanging Velocity

Distance (m)Distance (m)

Time (s)Time (s)

Speed upSpeed up

Slow Slow DownDown

Average VelocityAverage Velocity

When working with a constant When working with a constant velocity, we use the following equation.velocity, we use the following equation.

ννavgavg =Δx / Δt =Δx / Δt

VelocityVelocityDisplacementDisplacement

TimeTime

Δ = changeΔ = change

Sample Problem

What is the velocity of a runner that can What is the velocity of a runner that can travel 10 m in 5 seconds?travel 10 m in 5 seconds?

ννavgavg =Δx / Δt =Δx / Δt

ννavgavg = 10 m/5 s= 10 m/5 s

ννavgavg = 2 m/s = 2 m/s

Acceleration changes Acceleration changes velocityvelocity

Acceleration (a):Acceleration (a): the rate of change of the rate of change of velocity. velocity.

Objects can accelerate in both the + and - Objects can accelerate in both the + and - direction.direction.

Velocity

Time

Accelerating CarAccelerating Car

0

100

Constant acceleration

velocity

Time

Car on cruise controlCar on cruise control

0

100 Zero

Accelerationvelocity

Time

Negative Accelerating Negative Accelerating Car Car

0

100

- acceleration

velocity

Time

Acceleration (cont.)Acceleration (cont.)

aaavgavg = = Δ ν /ΔtΔ ν /Δt = = vvff – v – vii

ΔΔtt

accelerationaccelerationSI unit = m/sSI unit = m/s²²

Final Velocity

Initial Velocity

Sample ProblemA car traveling at 7.0 m/s accelerates uniformly to a velocity of 12.0 m/s in 2.0 s. What is the acceleration of the car?

VVii = 7 m/s= 7 m/s VVff = 12 m/s= 12 m/s

a = a = vvff – – vvii

ΔΔtt

t = 2.0 t = 2.0 ss

= = (12.0 m/s – 7.0 (12.0 m/s – 7.0 m/sm/s) =) =

2.0 s2.0 s

2.5 2.5 m/s²m/s²

Changing AccelerationChanging Acceleration

Velocity Velocity (v)(v) Time Time

((ΔΔt)t)

Forward Motion

Reverse Reverse MotionMotion

Zero Zero MotionMotion

1-Dimentional Motion 1-Dimentional Motion EquationsEquations

VVavgavg =Δx/Δt =Δx/Δt

Δx = Δx = ½½ (v (vi i ++ vvff) Δt) Δt

a = (va = (vf f - v- vii) / Δt) / Δt

Δx = vΔx = vii Δt + ½ aΔt² Δt + ½ aΔt²

vvff² = v² = vii² + 2aΔx² + 2aΔx