Acceleration
• Rate of change of velocity
Section 2-2
– Occurs when speed or direction changes
a =
avg
Acceleration
Δv v − v
=
Δt t − t
f
f
i
i
• m/s2
Acceleration
Velocity-time Graph
• Velocity on y-axis
• Has direction and magnitude
•Motion
Direction
•Forward
•Speed
change
•Increasing
•Forward
•Decreasing
•Backward
•Increasing
•Backward
•Decreasing
•Acceleration
Velocity-time Graph
• Time on x-axis
• Slope is the
acceleration
slope =
rise Δv
=
run Δt
Velocity-time Graph
• Instantaneous Velocity
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– Slope of the graph at any certain point
– Can be found by drawing a tangent line
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1
Velocity-time Graph
Velocity-time Graph
• Displacement
– The area under the curve
– May need to be found in parts
Velocity-time Graph
Velocity-time Graph
Acceleration-time Graph
Acceleration-time Graph
• Acceleration on
y-axis
• Time on x-axis
• Change in
Velocity
– Area under the
curve
– May need to be
done in parts
2
Acceleration-time Graph
Acceleration-time Graph
Acceleration-time Graph
Motion with
Constant Acceleration
• Also called uniform acceleration
• Equations only work for constant
acceleration
• Vi = 0 if object starts at rest
Motion with
Constant Acceleration
Δx
Δt
vi + v f
v =
avg
v =
avg
2
1
Δx = (v + v )Δt
2
i
f
v = v + a(Δt)
f
i
1
Δx = v (Δt) + a(Δt)
2
2
i
1
Δx = (v + v )Δt
2
i
Motion with
Constant Acceleration
f
2
2
v = v + 2aΔx
f
i
3
Vi=0
Example Problem
1
Δx = (v )Δt
2
• A person accelerates from 4.20 m/s to 5.00
m/s in a distance of 115 m. How long did
this take?
f
v = a(Δt )
f
1
Δx = a(Δt)
2
2
2
v = 2aΔx
f
Example Problem
• A falling object accelerates at 9.80m/s2. An
object is dropped from a 10.0 m tall
building. How long does it take to reach the
ground?
Example Problem
• The world record for a car’s acceleration
was from rest to 96km/hr in 3.07 seconds.
How far did the car travel?
4