Question

A car P is 300m behind a car B and both are traveling in the same direction at 25ms–¹. Neglecting the length of the cars.

(i) calculate the acceleration of P.

(ii) it's velocity at the moment of passing B.

(iii) The distance it has travelled in 20s.

Answer 1

(i)

$$v=v_0+at$$

$$a_B=\frac{\Delta v}{\Delta t}=\frac{27.5-25}{20}=0.125\:\rm m/s^2$$ $$d_P=d_B+300$$

$$v_0t+a_Pt^2/2=v_0t+a_Bt^2/2+300$$

$$a_P*20^2/2=0.125*20^2/2+300$$

$$a_P=1.625\;\rm m/s^2$$

(ii)

$$v_P=v_0+a_Pt\\ =25+1.625*20=57.5\:\rm m/s$$

(iii)

$$d_P=v_0t+a_Pt^2/2\\ =25*20+1.625*20^2/2=825\:\rm m$$