Question

A car is moving at 17.7 m/s when it begins to slow down with a deceleration of 2.5 m/s². How long does it take for the car to travel 80 meters as it slows down?

 

Answer 1

$$v(t)=\int adt=v_0+at$$

$$s(t)=\int vdt=\int (v_0+at)dt=s_0+v_0t+\dfrac{at^2}{2}$$

Given $a=-2.5\ m/s^2, v_0=17.7\ m/s,s _0=0\ m$

$$v(t_1)=0=>17.7-2.5t_1=0$$

$$t_1=7.08 \ s$$

$$s(t_1)=s(7.08)=0+17.7(7.08)-\dfrac{2.5(7.08)^2}{2}$$

$$=62.658 (m)$$

Car travels 62.658 meters and stop.

Therefore car cannot travel 80 meters.