An automobile with a mass of 1180 kg is traveling at a speed v = [06] m/s. a. What is its kinetic energy in SI units? b. What speed (m/s) must an 82.7-kg person move to have the same kinetic energy? c. At what speed (m/s) must a 12.1-g bullet move to have the same kinetic energy? d. What would be the speed (m/s) of the automobile if its kinetic energy were doubled?

Complete Question:

An automobile with a mass of 1180 kg is traveling at a speed v =2.51 m/s. What is its kinetic energy in SI units? What speed (m/s) must an 82.7-kg person move to have the same kinetic energy? At what speed (m/s) must is 12.1-g bullet move to have the same kinetic energy? What would be the speed (m/s) of the automobile if its kinetic energy were doubled?

a) 3717.1 J b) 9.48 m/s c) 783.8 m/s d) 3.55 m/s

Explanation:

a)

By definition, the kinetic energy of a mass m with a speed v, is as follows:

     

if m= 1180 Kg, and v= 2.51 m/s, the kinetic energy can be calculated as follows:

       

b)

If the kinetic energy must be the same, and m= 82,7 Kg, we can write the following expression:

       

We can solve the above equation as follows:

       

c)

If K remains the same, and m = 12.1 g = 0.0121 kg (in SI units). we can solve for v  as follows:

       

d)

Now, if the kinetic energy were doubled, we would have the following equation:

       

We can solve for the new speed v as follows:

       

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