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The position of a particle as a function...

The position of a particle as a function of time is described by relation `x = 3t - 3t^2 + t^3` where the quantities are expressed in SI units. If mass of the particle be 10 kg, the work done in first three seconds is

A

10 J

B

30 J

C

300 J

D

675 J

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `x= 3t - 3t^2 +t^3`
Velocity `v = (dx)/(dt) = 3 – 6t + 3t^2`
At `t=0, v_o = 3 m//s`, At t = 3
Velocity.va = 12 m/s
Work done = change in kinetic energy (work-energy theorem)
`=1/2m(v_3^2-v_0^2)=1/2xx10(12^2-3^2)`
`=1/2 xx10(144 - 9) = 5 xx135 = 675 J`
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Knowledge Check

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