Question

The front 1.20 m of a 1,250-kg car is designed as a "crumple zone" that collapses to absorb the shock of a collision.

(a) If a car traveling 26.0 m/s stops uniformly in 1.20 m, how long does the collision last?

___ s

(b) What is the magnitude of the average force on the car?

 ___N

(c) What is the magnitude of the acceleration of the car? Express the acceleration as a multiple of the acceleration of gravity.

 ___ g

Answer 1

Solution.

$L=1.20m;$

$m=1250kg;$

$v_0=26.0m/s;$

$v=0m/s;$

a) $L=\dfrac{v_0+v}{2}t\implies t=\dfrac{2L}{v+v_0};$

$t=\dfrac{2\sdot1.20}{26.0}=0.92s;$

b) $F=ma;$

$a=\dfrac{v-v_0}{t}$ ;

$a=\dfrac{0-26.0}{0.92}=-28.26 m/s^2;$

$F=1250\sdot28.26=35326N;$

c)$g=9.8m/s^2; a=2.88g;$

Answer: $a) t=0.92s;$

b)$F=35326N;$

c)$a=2.88g.$