Practice 2B: | 1
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Average acceleration- by
Jacobson˛ , 2005
1. As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at -4.1 m/s˛ as it slows from 9.0 m/s to 0 m/s. Find the time interval of acceleration for the bus.
Since we know aavg = -4.1 m/s˛ and Dv = -9.0 m/s (v
final – v initial), we can rearrange the average acceleration formula to solve
for t. aavg
= Dv/Dt becomes
Dt = Dv/ aavg . So Dt
= (-9.0 m/s)/( -4.1 m/s˛) = 2.2 s
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2. A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s˛ to reach a speed of 12 m/s. How long does it take for this acceleration to occur?
Dv
= v final – v initial = 12 – 7 = 5 m/s
and aavg = 2.5 m/s˛ , so plug in those values
into the formula Dt = Dv/ aavg . Dt = (5m/s)/(2.5 m/s˛) =
2 s
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3. With an average acceleration of -0.50 m/s˛, how long will it take a cyclist to bring a bicycle with an initial speed of 13.5 m/s to a complete stop?
Again, use the formula Dt = Dv/ aavg to find the answer. We know that v final = 0
m/s and that v initial is 13.5 m/s, so Dv
= v final – v initial = 0 – 13.5 = -13.5m/s. aavg = -0.50 m/s˛, so plug in the values.
Dt = (-13.5m/s)/(-0.50 m/s˛) = 27 s
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4. Turner’s treadmill runs with a velocity of -1.2 m/s and speeds up at regular intervals during the half-hour workout. After 25 min, the treadmill has a velocity of -6.5 m/s. What is the average acceleration of the treadmill during this period?
Using the average acceleration formula aavg = Dv/Dt , plug in the values that you know. Dv = -6.5m/s - -1.2m/s = -5.3m/s and Dt = (25min)(60sec/min) = 1500 s , so aavg =
(-5.3m/s)/(1500s) = -3.5 *
10 ^ -3 m/s˛
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5. Suppose a treadmill has an average acceleration of 4.7 * 10 ^ -3 m/s˛. a. How much does its speed change after 5.0 min? b. If the treadmill’s initial speed is 1.7 m/s, what will its final speed be?
a. First rearrange the average acceleration formula to solve for velocity. aavg = Dv/Dt becomes Dv = Dt aavg . Dt = (5.0min)(60s/min) = 300s , so Dv = (300s)(4.7 * 10 ^ -3 m/s˛) = 1.4 m/s
b. Since Dv = vf - vi
, you can solve for the final velocity by adding the initial velocity and
the change in velocity you found in part a.
vf = 1.7 m/s + 1.4 m/s = 3.1
m/s
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