# The kinetic energy of an object with a mass of 2 kg constantly changes from 32 J to 84 J over 4 s. What is the impulse on the object at 1 s?

Apr 21, 2016

$F \cdot \Delta t = 2 , 1 \text{ } N \cdot s$

#### Explanation:

$\tan \theta = \frac{84 - 32}{4}$

$\tan \theta = \frac{52}{4} = 13$
$E = \frac{1}{2} \cdot m \cdot {v}^{2} \text{ "v^2=(2E)/m" ; "v=sqrt((2E)/m)" ; } v = \sqrt{E}$
$t = 0 \text{ "E=32J" } v = 5 , 66 \frac{m}{s}$
$t = 1 \text{ "E=32+13=45J" } v = 6 , 71 \frac{m}{s}$
$t = 2 \text{ "E=45+13=58J" } v = 7 , 62 \frac{m}{s}$
$t = 3 \text{ "E=58+13=71J" } v = 8 , 43 \frac{m}{s}$
$t = 4 \text{ "E=71+13=84J" } v = 9 , 17 \frac{m}{s}$

$\text{impulse for t=1 }$
$F \cdot \Delta t = m \left(v \left(1\right) - v \left(0\right)\right)$

$F \cdot \Delta t = 2 \left(6 , 71 - 5 , 66\right)$
$F \cdot \Delta t = 2 \cdot 1 , 05$
$F \cdot \Delta t = 2 , 1 \text{ } N \cdot s$