A moving object has a kinetic energy of 146 J and a momentum of 23.4 kg·m/s.

a) Find the speed of the object. Answer in units of m/s.

.5 m v^2 = 146 = .5 mv v

m v = 23.4

so
146 = .5 (23.4) v

v = 146/11.7

To find the speed of the object, we need to use two formulas: one for kinetic energy and one for momentum. The formulas are:

1. Kinetic energy (KE) = (1/2)mv^2
2. Momentum (p) = mv

Given that the object has a kinetic energy of 146 J and a momentum of 23.4 kg·m/s, we can set up the following equations:

1. 146 = (1/2)m(v^2)
2. 23.4 = mv

From equation 2, we can solve for m (mass):

m = p/v

Substituting the value of momentum (p = 23.4 kg·m/s) and rearranging the formula:

23.4 = mv
m = 23.4 / v

Now, substituting this value of m into equation 1:

146 = (1/2)(23.4 / v)(v^2)

Simplifying this equation, we get:

146 = (11.7/v)(v^2)
146 = 11.7v

Dividing both sides of the equation by 11.7:

v = 146 / 11.7

Calculating this, we find:

v ≈ 12.47 m/s

Therefore, the speed of the object is approximately 12.47 m/s.