# The velocity of an object with a mass of 3 kg is given by v(t)= 6 t^2 -4 t . What is the impulse applied to the object at t= 3 ?

Feb 13, 2016

$F \cdot t = 3 \cdot 42 = 126 N . s$

#### Explanation:

$F = \frac{d P}{d t}$
$F \cdot d t = d P$
$F \cdot d t = d \left(m v\right)$
$F \cdot d t = m d v$
$d v = \left(12 t - 4\right) \cdot d t$
$F \cdot d t = m \cdot \left(12 t - 4\right) \cdot d t$
$\int F \cdot d t = \int m \cdot \left(12 t - 4\right) \cdot d t$
$F \cdot t = m \int \left(12 t - 4\right) \cdot d t$
$F \cdot t = 3 \left(6 {t}^{2} - 4 t\right)$
$F \cdot t = 3 \left(54 - 12\right)$
$F \cdot t = 3 \cdot 42 = 126 N . s$