The equation of displacement of a particle along the X-axis is `x = 40 + 12t - t^(3)` . How much distance does it travel before stop?

Options

A. 16 m
B. 40 m
C. 56 m
D. 36 m

Answer

C

Explanation

x = 40 12t-`t^(3) " ""or", (dx)/(dt) =12 12-3 t^(3)`
After time t s if the particle comes of rest then
0 = 12 -3`t^(2) " ""or",t^(2)=4 " ":. ` t = 2 s
The distance travelled by the particle is 2 s,
`x|_(t=2)=40+12xx2-8=56` unit