The coordinates of a body moving in a plane at any instant of time `t` are `x=alphat^(2)` and `y=betat^(2)`. The speed of the body is.

Explanation

To find the speed of a body moving in a plane with given coordinates \( x = \alpha t^2 \) and \( y = \beta t^2 \), we can follow these steps:

### Step 1: Differentiate the coordinates with respect to time
We need to find the velocities in the x and y directions by differentiating the coordinates with respect to time \( t \).

- For \( x \):
\[
\frac{dx}{dt} = \frac{d}{dt}(\alpha t^2) = 2\alpha t
...