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.)

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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