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

`v = 14.78m/s`

Step-by-step explanation:

Given

`KE = 150J`

`p = 20.3kgm/s`

Required

Determine the object's speed

Kinetic Energy is calculated as:

`KE = (1)/(2)mv^2`

Make m the subject

`m = (2KE)/(v^2)`

Momentum is calculated as:

`p = mv`

Make m the subject

`m = (p)/(v)`

So, we have:

`m = (p)/(v)` and
`m = (2KE)/(v^2)`

Equate both expressions:
`m = m`

`(2KE)/(v^2) = (p)/(v)`

Multiply both sides by v

`v * (2KE)/(v^2) = (p)/(v)*v`

`(2KE)/(v) = p`

Make v the subject

`v = (2KE)/(p)`

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

`v = (2 * 150)/(20.3)`

`v = (300)/(20.3)`

`v = 14.78m/s`