Home
Class 11
PHYSICS
The motion of a particle along a straigh...

The motion of a particle along a straight line is described by equation : `x = 8 + 12 t - t^3` where `x` is in metre and `t` in second. The retardation of the particle when its velocity becomes zero is.

A

`24ms^(-2)`

B

zero

C

`6ms^(-2)`

D

`12ms^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`x = 8 + 12t - t^3`
`v = (dx)/(dt) = 12 - 3t^2 = 0 rArr t = 2sec`
`a = (dv)/(dt) = - 6t`
at t = 2sec , ` a= -12m//s^2`
Promotional Banner

Similar Questions

Explore conceptually related problems

The motion of a particle along a straight line is described by the equation: x=8+12t-t^(3) , where x is inmeter and t in second. (i) the initial velocity of particle is 12 m//s (ii) the retardation of particle when velocity is zero is 12 m//s^(2) (iii) when acceleration is zero, displacement is 8 m the maximum velocity of particle is 12 m//s

The displacement of a particle moving in a straight line, is given by s = 2t^2 + 2t + 4 where s is in metres and t in seconds. The acceleration of the particle is.

The motion of a particle along a straight line is described by the function x=(2t -3)^2, where x is in metres and t is in seconds. Find (a) the position, velocity and acceleration at t=2 s. (b) the velocity of the particle at the origin .

The displacement of a particle moving in a straight line is described by the relation s=6+12t-2t^(2) . Here s is in metre and t in second. The distance covered by the particle in first 5s is

A particle moves along a straight line such that its position x at any time t is x=3t^(2)-t^(3) , where x is in metre and t in second the

The displacement x of particle moving in one dimension, under the action of a constant force is related to the time t by the equation t = sqrt(x) +3 where x is in meters and t in seconds . Find (i) The displacement of the particle when its velocity is zero , and (ii) The work done by the force in the first 6 seconds .

The displacement of a particle is represented by the equation, s=3 t^3 =7 t^2 +4 t+8 where (s) is in metres and (t) in seconds . The acceleration of the particle at t=1 s is.

The distance x of a particle moving in one dimensions, under the action of a constant force is related to time t by the equation, t=sqrt(x)+3 , where x is in metres and t in seconds. Find the displacement of the particle when its velocity is zero.

A particle moves in x-y plane according to the equations x= 4t^2+ 5t+ 16 and y=5t where x, y are in metre and t is in second. The acceleration of the particle is