Home
Class 12
PHYSICS
Displacement (x) of a particle is relate...

Displacement (x) of a particle is related to time (t) as
`x = at + b t^(2) - c t^(3)`
where a,b and c are constant of the motion. The velocity of the particle when its acceleration is zero is given by:

A

`a + (b^(2))/(c )`

B

`a + (b^(2))/(3c)`

C

`a + (b^(2))/(4c)`

D

`a + (b^(2))/(2c)`

Text Solution

Verified by Experts

The correct Answer is:
B
`x(t) = at + bt^(2) - ct^(3), v = (dx(t))/(dt) = a + 2bt - ct^(2)`
`a = (d^(2) x (t))/(dt^(2)) = 2b - 6ct, a = 0]`
`g = (b)/(3c), v = a + 2b ((b)/(3c)) - 3c ((b)/(3c))^(2), v = a + (b^(2))/(3c)`
Promotional Banner

Similar Questions

Explore conceptually related problems

The displacement x of a particle varies with time t as x = ae^(-alpha t) + be^(beta t) . Where a,b, alpha and beta positive constant. The velocity of the particle will.

The displacement (x) of a particle as a function of time (t) is given by x=asin(bt+c) Where a,b and c are constant of motion. Choose the correct statemetns from the following.

A particle moves along x-axis and its displacement at any time is given by x(t) = 2t^(3) -3t^(2) + 4t in SI units. The velocity of the particle when its acceleration is zero is

The displacement of a particle after time t is given by x = (k // b^(2)) (1 - e^(-bi)) . Where b is a constant. What is the acceleration fo the particle ?

The displacement x of a particle at time t moving along a straight line path is given by x^(2) = at^(2) + 2bt + c where a, b and c are constants. The acceleration of the particle varies as

Displacement x=t^(3)-12t+10 . The acceleration of particle when velocity is zero is given by

For a particle moving in a straight line, the displacement of the particle at time t is given by S=t^(3)-6t^(2) +3t+7 What is the velocity of the particle when its acceleration is zero?

The displacement of a particle at time t is given by vecx=ahati+bthatj+(C )/(2)t^(2)hatk where a, band care positive constants. Then the particle is