speed vs.velocity speed (s) is the distance an object travels per unit of time (rate). speed (s) is...
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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.
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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.
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Constant / Zero Velocity Constant / Zero Velocity
Distance (m)Distance (m)
Time (s)Time (s)
Constant velocityConstant velocity
Zero VelocityZero Velocity
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Changing VelocityChanging Velocity
Distance (m)Distance (m)
Time (s)Time (s)
Speed upSpeed up
Slow Slow DownDown
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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
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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
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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
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Accelerating CarAccelerating Car
0
100
Constant acceleration
velocity
Time
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Car on cruise controlCar on cruise control
0
100 Zero
Accelerationvelocity
Time
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Negative Accelerating Negative Accelerating Car Car
0
100
- acceleration
velocity
Time
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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
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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
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Changing AccelerationChanging Acceleration
Velocity Velocity (v)(v) Time Time
((ΔΔt)t)
Forward Motion
Reverse Reverse MotionMotion
Zero Zero MotionMotion
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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