The kinetic energy of an object with a mass of 3 kg constantly changes from 60 J to 270 J over 8 s. What is the impulse on the object at 5 s?

Mar 28, 2016

$3 \cdot \left(5 \cdot \frac{\sqrt{180} - \sqrt{40}}{8} - \sqrt{40}\right)$

Explanation:

t=0, ${v}_{1} = \sqrt{2 \cdot \frac{W}{m}}$
${v}_{1} = \sqrt{40}$
t=8, ${v}_{1} = \sqrt{2 \cdot \frac{W}{m}}$
${v}_{1} = \sqrt{180}$
first, we calculate acceleration
$a = \frac{{v}_{1} - {v}_{2}}{t}$
$a = \frac{\sqrt{180} - \sqrt{40}}{8}$
velocity at t=5
$v = a \cdot t$
$a = 5 \cdot \frac{\sqrt{180} - \sqrt{40}}{8}$
impulse on the object
$m \cdot \Delta v$
$3 \cdot \left(5 \cdot \frac{\sqrt{180} - \sqrt{40}}{8} - \sqrt{40}\right)$

Mar 28, 2016