Question

An object is moving so that its kinetic energy is 238 J and the magnitude of its momentum is 20.1 kg · m/s. Determine the speed of the object. Answer in units of m/s.

Answer 1

To solve this problem we will apply the concepts related to kinetic energy and the value of momentum. Both variables are dependent on the mass and velocity of the object. By dividing between the two terms we can clear the speed of the object and find its value. Let's proceed to define the kinetic energy, for which,

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

Here,

m = mass

v = Velocity

The expression of momentum of a object is given as

$p = mv$

If we divide two expression we have that

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

$\frac{KE}{p} = \frac{1}{2} v$

Rearrange to find the velocity we have that

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

Replacing we have that

$v = \frac{2(238)}{20.1}$

$v = 23.68m/s$

Therefore the speed of the object is 23.68m/s