A particle moves along x-axis such that its position veries with time as `x=50t-5t^2`. Select the correct alternative (s).

Options

A. The particle has travelled 130m distance by `t=6s`.
B. At `t=4s` and `t=12s`, the particle is at 120 m distance from starting point.
C. the particle will never be at a distance of 130 m from starting point.
D. During the whole motion, the particle does not have same velocity at 2 different instants.

Answer

A, B, D

Explanation

`x=50t-5t^2`
`v=(dx)/(dt)=50-10t`
Put `v=0impliest=5s`
at `t=5`:`x_1=50xx5-5(5)^2=125`m
at `t=4s`: `x_2=50xx4-5(4)^2=120`m
at `t=6s: `x_3=50xx6-5(6)^2=120`m
at `t=12s`: `x_4=50xx12-5(12)^2=-120` m
Distance travelled in 6 s:
`AC+CB=125+5=130`m
Velocity at no two points has same magnitude and direction. Finally particle will continue to move towards left and its distance from origin will go on increasing.