1. Velocity and Acceleration

2. Speed vs.Velocity
Speed is the distance an object travels per unit of time (rate).
Scalar quantity- Tells magnitude of an object.
Velocity describes the speed and direction of a moving object.
Vector quantity- tells magnitude and direction.

3. Displacement Defines the distance and direction between two positions.
Distance: Length of the displacement vector.
Time interval- Distance between t0 and t1.
Common symbol is Δt
ΔT=t1-t0
SI Unit is m/s

4. Velocity
Objects undergoing motion will either have a constant or changing velocity
At a constant velocity, an object neither speeds up or slows down.
At a changing velocity, an object will either speed up or slow down.

5. Constant / Zero Velocity
Distance (m)
Time (s)
Zero Velocity
Constant velocity

6. Average Velocity νavg =Δd / Δt
When working with a constant velocity, we use the following equation.
νavg = Δx / Δt
νavg =Δd / Δt
Velocity
Distance
Time
Δ = change

7. Sample Problem
What is the velocity of a runner that can travel 10 m in 5 seconds?
νavg =Δd / Δt
νavg = 10 m/5 s
νavg = 2 m/s

8. Changing Velocity
Distance (m)
Time (s)
Changing velocity

9. Acceleration changes velocity
Acceleration is the rate of change of velocity within a given time interval.
Objects can accelerate in both the positive and negative direction. d t d t v v

10. Graphing Acceleration
Velocity (v)
Time (t)

11. Accelerating Car
100
velocity
Time
Constant acceleration

12. Car on cruise control
100
velocity
Time
Zero Acceleration

13. Decelerating Car
100
velocity
Time
deceleration

14. Acceleration (cont.) aavg = Δ ν /Δt = vf – vi t Final Velocity
Initial Velocity
aavg = Δ ν /Δt = vf – vi t
acceleration
SI unit = m/s²

15. Sample Problem
A 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?
2.5 m/s²
a = vf – vi t
= (12.0 m/s – 7.0 m/s) =
2.0 s
Vf = 12 m/s
Vi = 7 m/s
t = 2.0 s