# 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

#### Explanation:

Impulse is defined as the force exerted over a time interval. Asking what the impulse is at a specific instant of time makes no sense. Impulse is equivalent to the total change in momentum. It is often useful when we know an initial and final velocity, but we don't know if the change was made because of a small force acting over a long time, or a large force acting very quickly.

One could ask about the velocity, acceleration, or force at an instant of time. Each of these would be answerable with the information provided. One could also ask about the total impulse exerted over the first 5 seconds. If one of those questions was the one you trying to answer, please submit another question.