A man is driving out of his driveway by backing up. He realizes he has forgotten his lunch, so he pulls back into the driveway. Car experts agree that the best way to do this is to press on the brake until the car comes to a complete stop, shift from reverse into first gear, then accelerate forward.
The driver, however, shifts into first gear while the car is rolling backward and pushes on the accelerator until he is going forward. This causes some wear on the transmission. The following chart shows some data about his progress. (Negative velocity = backwards)
t(s) x(m) v(m/s)
0.0 1.35 –1.8
0.5 0.60 – 1.2
1.0 0.15 – 0.6
1.5 0.00 0.0
2.0 0.15 0.6
2.5 0.60 1.2
3.0 1.35 1.8
(i)What is the value of his average velocity?
Text Solution
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Ans.
(i)
Sol. The average velocity is v avg = Δ x/ Δ t. The net displacement is
Δ x = 1.35 m – 1.35 m = 0 m
(ii)
Sol. This question consists entirely of words, but let us write an equation anyway. Uniform acceleration means a is constant, and a = Δ x/ Δ t. Thus Δ v and Δ t are in a constant ratio. If one of the choices express this fact, than that would be the solution. (If not, we will have to think some more, perhaps find another equation). D is the correct answer.
(iii)
Sol. For any 0.5 s interval in the chart, the acceleration ( Δ v/ Δ t) is a constant 1.2 m/s 2 , even for the intervals near t = 1.5 s, where the velocity is zero. Thus B is the right answer.
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