A car starts from rest and moves with a constant acceleration of `5 m//s^2` for 10 s before the driver applies the brake. It then decelerates for 5 s before coming to rest, then the average speed of the car over the entire journey of the car is

Options

A. 23 m/s
B. 30 m/s
C. 33 m/s
D. 25 m/s

Answer

D

Explanation

Schematic diagram for motion of body is

Average speed = Total displacement/toal time
In intercal t = 0 to t = 10 s,
Displacement , ` s_1 = 1/2 a_1t^2 =1/2 xx 5 xx (10)^2 = 250 m`
Final velocity , ` v_1 = u + a_1t`
`rArr v_1 = 0+ 5 xx 10 = 50 ms^(-1)`
In interval , t = 10 s to t = 15 s,
`v_1 = 50 ms^(-1), v_2 = 0 ms^(-1) , t = 5s`
Using v = u + at
We have , `a_2 = (0-50)/(5) = - 10 ms^(-2)`
And by `v^2 - u^2 = 2as , `we have
`v_2^2 - v_1^2 = 2(a_2)s_2 rArr s_2 = (50 xx 50)/(2 xx 10) = 125 m`
So average speed for interval , t = 0 to t = 15 s ,
We have
`V_(avg) = (s_1 + s_2)/(t_1 + t_2) = (250 + 125)/(10 + 5) = 375 / 15 = 25 ms^(-1)`