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## A car going initially with a velocity 13.5 m/s accelerates at a rate of 1.9 m/s 2 for 6.2 s. It then accelerates at a rate of -1.2 m/s2 unti

Question

A car going initially with a velocity 13.5 m/s accelerates at a rate of 1.9 m/s 2 for 6.2 s. It then accelerates at a rate of -1.2 m/s2 until it stops. a) Find the car’s maximum speed b) Find the total time from the start of the first acceleration until the car is stopped c) What’s the total distance the car travels?

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Physics
6 months
2021-07-28T14:40:45+00:00
2021-07-28T14:40:45+00:00 1 Answers
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## Answers ( )

(a)For the first 6.2 s, the car has velocity at timetgiven byso that after 6.2 s, it attains a velocity of

For any time

tafter 6.2 s, its velocity is given bywhich tells us the velocity only falls from this point onward. This means the maximum speed is 25.28 m/s, or about

25.3 m/s.(b)Solve fort(after 6.2 s) that makesv(t)= 0 :It takes the car about 21.2 s to come to a rest, so the car travels a total of about 6.2 s + 21.2 s =

27.4 s.(c)For the first 6.2 s, the car undergoes a displacement at timetofFor time

tbeyond 6.2 s, its displacement isThe car comes to a rest after 21.2 s (accelerating at a rate of -1.2 m/s^2), so that its total displacement is

so the car travels a total distance of about

387 m.