Two particles `P` and `Q` start from rest and move for equal time on a straight line. Particle `P` has an acceleration of `X m//s^2` for the first half of the total time and `2 X m//s^2` for the second half. The particle `Q` has an acceleration of `2 X m//s^2` for the first half of the total time and `X m//s^2` for the second half. Which particle has covered longer distance ?

Options

A. both have covered the same distance
B. `P` has covered the larger distance
C. `Q` has covered the larger distance
D. none of these

Answer

C

Explanation

For `P`, in `t` sec.
`x_1 = (1)/(2) X t^2 = (Xt^2)/(2) rArr v_1= Xt`
`x_2 = (Xt)t + (1)/(2) 2 X t^2 rArr x_2 = 2 Xt^2`
`x_p = x_1 + x_2 = (5)/(2) X + 2`
For `Q`,
`y_1 = (1)/(2) (2 X) t^2 = X t^2 rArr v_2 = 2 Xt`
`y_2 = (2 Xt) t + (1)/(2) X t^2 = (5)/(2) X t^2`
`y_Q = y_1 + y_2 = (7)/(2) X t^2 rArr y_Q gt x_p`.