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Question

If the distance ‘s’ metre traversed by a particle in t seconds is given by s=t33t2, then the velocity of the particle when the acceleration is zero, in metre/sec is,


A

3

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B

-2

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C

-3

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D

2

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Solution

The correct option is C

-3


Step 1: Given data

The distance ‘s’ metre traversed by a particle in t seconds is, s=t33t2

Step 2: Formula used

The first derivative of displacement is velocity

That is, v=dsdt

Acceleration(a) is the derivative of velocity with respect to time.

That is, a=dvdt

In other words, acceleration(a) is the second derivative of displacement(s).

That is, a=d2sdt2

Step 3: Find Velocity (v):

Velocity(v) is the rate of change of distance of an object with respect to time.

Here, s=t33t2

Velocity, v=dsdt

That is,

v=d(t3-3t2)dtv=3t2-3×2tv=3t2-6t.....(1)

Step 4: Find Acceleration (a):

Acceleration(a) is the rate of change of the velocity of an object with respect to time.

Acceleration, a=dvdt

That is,

a=d(3t2-6t)dta=2×3t-6a=6t-6....(2)

Step 5: Find Velocity at a=0:

To find the time t where the acceleration becomes zero, equate the equation (2) to zero

a=6t-60=6t-66=6t66=t1=t

That is, t=1

Substitute this in equation (1)

v=3t2-6tv=3×12-6×1v=3-6v=-3ms-1

Therefore, the velocity of the particle when the acceleration is zero, in metre/sec is -3ms-1.


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