Please help me question 2.34 & question 2.37 in Physic 139. The figure below sho

Question

Please help me question 2.34 & question 2.37 in Physic 139.
The figure below shows a plot of velocity versus time for an object in linear motion, (a) Compute the acceleration for each phase of motion, (b) Describe how the object moves during the last time segment? At a sports car rally, a car starting from rest accelerates uniformly at a rate of 9.0 m/s^2 over a straight line distance of 100 m. The time to beat in this event is 4.5 s. Does the driver beat this time? If not, what must the minimum acceleration be to do so?

Explanation / Answer

2.34 :

(A) slope of v vs t curve gives the acceleration.

0 to 1 sec:

a = 0

1 to 3 s:

a = 4 m/s^2

3 to 8s:

a = - 12 - 8 / (8 - 3) = - 4 m/s^2

8 to 9s:

a = -4 - (-12) / 1 = 8 m/s^2

9 to 11s:

a = 0

(b) object moves with constant velocity in opposite direction /

2.37 :

a = 9 m/s^2

d = 100 m

d = v0 t + a t^2 /2

100 = 0 + 9 t^2 /2

t = 4.71 sec

So Driver does not beat the time.

For minimum acceleration,

100 = 0 + a(4.5^2 ) / 2

a = 9.88 m/s^2

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