# The velocity of an object with a mass of 3 kg is given by v(t)= 3 t^2 - 5 t . What is the impulse applied to the object at t= 2 ?

Dec 19, 2015

$6 \text{N.s}$

#### Explanation:

The impulse is the average force x time

The average force id given by:

${F}_{\left(a v e\right)} = \frac{m \Delta v}{t}$

So the impulse = $m \Delta \frac{v}{\cancel{t}} \times \cancel{t}$

$= m \Delta v$

$v \left(t\right) = 3 {t}^{2} - 5$

So after 2s:

$v = 3 \times {2}^{2} - 5 \times 2 = 2 \text{m/s}$

Assuming the impulse is over a period of 2s then $\Delta v = 2 \text{m/s}$

$\therefore$ Impulse$= 3 \times 2 = 6 \text{N.s}$