The front 1.20 m of a 1400 - kg car is designed as a “crumple zone” that collapses to absorb the shock of a collision. If a car traveling 25.0 m/s stops u niformly in 1.20 m

Question

(a) how long does the collision last, (b) what is the magnitude of the average force on the car, and (c) what is the magnitude of the acceleration of the car? Express the acceleration as a multiple of the acceleration due to gravity.

Answer 1

Assuming the car collapses completely, s = 1.2 m

a) _{t can be obtained first by using s = v average * t. the average velocity of 12.5 m/sec. gives t= 1.2/12.5 = .096 sec.}

^{b) the magnitude of the force F, can be obtained by using the impulse = delta p or impulse I = 25*1400 = 35000 N sec. Using I = F * t, This leads to an average force F = I/t = 364583 N}

^{c) Using F= ma, gives an acceleration of a = F/m = 364583/1400 = 260.42 m /sec2. which is 26.5 g.}