A car is moving with uniform velocity `10 m//s`. After `t = 5 sec`, brakes are applied to produce constant retardation and car comes to rest at `t = 10 sec`. The position time graph from `t = 0` to `15 s` is.

Options

A. .
B. .
C. .
D. .

Answer

A

Explanation

`x = 10 t`
`0 lt t 5 sec` for `t = 5 sec`,
`x_1 = 50 m`
`0 = 10 - a(10 - 5) rArr a = 2 m//s^2`
`x - x_1 = 10(t - 5) - (1)/(2) a(t - 5)^2 (5 lt t lt 10)`
`rArr x = 50 + 10 t - 50 - t^2 - 25 + 10 t`
`x = -t^2 + 20t - 25`
at `t = 10 , x_2 = 75 m` for `t gt 10 sec`
x = 75 m`.