Answer to Question #201281 in Mechanics | Relativity for Thobeka

Question

A driver of an ambulance going 70km/hr suddenly sees another car 35.0 m ahead. It takes the driver 0.62 s before he applies the brakes. Once he begins to brake, he reduces speed at a rate of 13.0 m/second squares. Determine if the driver will hit the car or not

Answer 1

$a=\frac{v-v_0}{t}=13$ m/s²

Time of breaking:

$t=\frac{v-v_0}{a}=70/(3.6\cdot13)=1.5\ s$

Breaking distance:

$d=70\cdot0.62/3.6+v_0t-at^2/2$

$d=70\cdot0.62/3.6+70\cdot1.5/3.6-13\cdot1.5^2/2=26.6\ m$

Since distance d < 35 m, the driver will not hit the car.