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Velocity-time equation of a particle mov...

Velocity-time equation of a particle moving in a straight line is, `v=(10+2t+3t^2)` (SI units) Find
(a) displacement of particle from the mean position at time `t=1s,` if it is given that displacement is 20m at time `t=0`.
(b) acceleration-time equation.

Text Solution

Verified by Experts

The correct Answer is:
A
(a) The given equation can be written as,
`v=(ds)/dt=(10+2t+3t^2) or ds=(10+2t+3t^2)dt`
or `int_20^s ds=int_0^1 (10+2t+3t^2)dt` or `s-20=[10t+t^2+t^3]_0^1`
or `s=20+12=32m`
(b) Acceleration-time equation can be obtained by differentiating the given equation w.r.t. time.
Thus, `a=(dv)/dt=d/dt(10+2t+3t^2)` or `a=2+6t`
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Knowledge Check

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