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A particle is moving in a straight line....

A particle is moving in a straight line. Its displacement at any instant t is given by `x = 10 t+ 15 t^(3)`, where x is in meters and t is in seconds. Find
(i) the average acceleration in the intervasl t = 0 to t = 2s and
(ii) instantaneous acceleration at t = 2 s.

Text Solution

AI Generated Solution

To solve the problem, we need to follow these steps: ### Step 1: Write down the displacement equation The displacement of the particle is given by: \[ x(t) = 10t + 15t^3 \] ### Step 2: Find the velocity by differentiating the displacement To find the velocity \( v(t) \), we differentiate the displacement equation with respect to time \( t \): ...
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