Question

A particle moving in a straight line its displacement at any instant t is given by x=10t+15t^2 here x is in m and t is in sec find instantaneous in t=2sec

Answer 1

instantaneous velocity=DX/dt =1
0+30t. at t=2sec. v=10+30(2)=70m/s

Answer 2

A particle moving in a straight line its displacement at any instant t is given by x=10t+15t². Its instantaneous velocity at t = 2 seconds is 70 m/s

Explanation:

Given

The displacement function of the particle

$x=15t^2+10t$

We know that instantaneous velocity is given by rate to change of displacement

Therefore,

$v=\frac{dx}{dt}$

$\implies v=\frac{d}{dt}(15t^2+10t)$

$\implies v=30t+10$

Velocity at t = 2 seconds

$v\Bigr|_{t=2}=30\times 2+10=70$ m/s

Thus, the instantaneous velocity is 70 m/s

Hope this answer is helpful.

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