A particle moves with a velocity v(t)=`(1/2)kt^(2)` along a straight line . Find the average speed of the particle in a time t.

Explanation

To find the average speed of a particle moving with a velocity given by \( v(t) = \frac{1}{2} kt^2 \) over a time interval from \( 0 \) to \( t \), we will follow these steps:

### Step 1: Understand the formula for average speed
The average speed \( v_{\text{avg}} \) is defined as the total distance traveled divided by the total time taken. Mathematically, it can be expressed as:
\[ v_{\text{avg}} = \frac{\text{Total Distance}}{\text{Total Time}} \]

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