Worked Example

Problem:
A particle has velocity:

$$ v = 4t $$

Find displacement as a function of time.

Solution

We know:

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

So,

$$ dx = 4t \, dt $$

Integrating:

$$ x = \int 4t \, dt = 2t^2 + C $$

If initial position is zero, then $C = 0$:

$$ x = 2t^2 $$