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.

Explanation

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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