The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of - 5.65 m/s2 for 4.00 s, making straight skid marks 62.9 m long, all the way to the tree. With what speed (in m/s) does the car then strike the tree?

Question

Mathematics

Jorge

6 May, 16:14

The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows uniformly with acceleration of - 5.65 m/s2 for 4.00 s, making straight skid marks 62.9 m long, all the way to the tree. With what speed (in m/s) does the car then strike the tree?

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Answers (1)

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Autumn Gray · Answer 1

Answer: the speed with which the car strikes the tree is 27.025 m/s

Step-by-step explanation:

We would apply Newton's equation of motion. It is expressed as

S = ut + 1/2at²

Where

S represents the distance covered by the car

u represents the initial velocity of the car (the speed with which the car strikes the tree)

t represents the time taken to cover the distance

a represents the deceleration of the car.

From the information given,

S = 62.9 meters

a = - 5.65 m/s2

t = 4 seconds

Therefore

62.9 = u * 4 + 1/2 * - 5.65 * 4²

62.9 = 4u - 45.2

4u = 62.9 + 45.2

4u = 108.1

u = 108.1/4 = 27.025 m/s