Answer to Question #206633 in Math for Festus

Question

A car move at a constant velocity of 20m/s for 10seconds and then accelerated uniformly to a velocity of 30m/s over 15 seconds. Calculate the distance covered during the motion

Answer 1

$$s_1=v_1t_1$$

$$s_1=20\ m/s\cdot 10s=200\ m$$

$$v_2=v_1+at_2$$

$$a=\dfrac{v_2-v_1}{t_2}$$

$$s_2=v_1t_2+\dfrac{at_2^2}{2}=v_1 t_2+\dfrac{(v_2-v_1)t_2}{2}$$

$$s_2=20 \ m/s\cdot15\ s+\dfrac{(30 \ m/s-20 \ m/s)15\ s}{2}=375\ m$$

$$s=s_1+s_2$$

$$s=200\ m+375\ m=575\ m$$

The distance covered during the motion is 575 metres.