Question

A moving object has a kinetic energy of 150J and a momentum of 20.3kgxm/s find the speed of the object in m/s

Answer 1

Answer:

$v = 14.78m/s$

Explanation:

Given

$KE = 150J$

$p = 20.3kgm/s$

Required

Determine the object's speed

Kinetic Energy is calculated as:

$KE = \frac{1}{2}mv^2$

Make m the subject

$m = \frac{2KE}{v^2}$

Momentum is calculated as:

$p = mv$

Make m the subject

$m = \frac{p}{v}$

So, we have:

$m = \frac{p}{v}$ and $m = \frac{2KE}{v^2}$

Equate both expressions: $m = m$

$\frac{2KE}{v^2} = \frac{p}{v}$

Multiply both sides by v

$v * \frac{2KE}{v^2} = \frac{p}{v}*v$

$\frac{2KE}{v} = p$

Make v the subject

$v = \frac{2KE}{p}$

Substitute $KE = 150J$ and $p = 20.3kgm/s$

$v = \frac{2 * 150}{20.3}$

$v = \frac{300}{20.3}$

$v = 14.78m/s$