An automobile having a mass of 480 kg is driven into a brick wall in a safety test. The bumper behaves like a spring of constant 6.49 × 106 N/m and compresses 4.62 cm as the car is brought to rest. What was the speed of the car before impact, assuming no energy was lost during impact with the wall? Answer in units of m/s

24.99 m/s

Explanation:

From the question,

The kinetic energy of the automobile before the impact = Energy stored in bumper after impact.

1/2mv² = 1/2ke² Equation 1

Where m = mass of the automobile, v =  speed of the car before impact, k = spring constant of the bumper, e = compression of the bumper after impact.

make v the subject of the equation

v = √(ke²/m) Equation 2

Given: k = 6.49×10⁶ N/m, e = 4.62 cm = 0.0462 m, m = 480 kg.

Substitute into equation 2

v = √(0.0462×6.49×10⁶/480)

v = √(624.6625)

v = 24.99 m/s.

Hence the speed of the car before impact = 24.99 m/s

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