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Analysis of an accident scene indicates a car was traveling at a velocity of 70.0 mph (31.3 m/s) along the positive x-axis at the instant the brakes were applied and then traveled a distance of 115 m before hitting an obstacle at a velocity of 4.65 m/s. Determine the car's acceleration a (assumed constant) and the time t between applying the brakes and hitting the obstacle. (Assume the car is moving in the positive direction. Indicate the direction with the sign of your answer.)

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Answer:

The acceleration of the car is -4.166 m/s²

The time between applying the brakes and hitting the obstacle is 6.4 s

Explanation:

Given;

initial velocity of the car when the brake was applied, u = 31.3 m/s

final velocity of the car after hitting an obstacle, v = 4.65 m/s

distance traveled before stopping, s = 115 m

The acceleration of the car is given by;

v² = u² + 2as

2as = v² - u²

a = (v² - u²) / 2s

a = (4.65² - 31.3²) / (2 x 115)

a = -4.166 m/s²

The time between applying the brakes and hitting the obstacle;

v = u + at

at = v - u

t = (v - u) / a

t = (4.65 - 31.3) / -4.166

t = 6.4 s

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