Question

A 15.0object moving at 7.50 meters per second on a horizontal, frictionless surfaceWhat is the total work that must be done on the object to increase its speed to 11.5 meters per second?

Answer 1

Given:

The mass of the object, m=15.0 kg

The initial velocity of the object, u=7.50 m/s

The increased velocity of the object, v=11.5 m/s

To find:

The work that must be done.

Step-by-step explanation:

The work needed to increase the velocity of an object is equal to the change in the kinetic energy of the object.

Thus the work that must be supplied to the object to increase its velocity to the given rate is,

`\begin{gathered} W=(1)/(2)mv^2-(1)/(2)mu^2 \\ =(1)/(2)m(v^2-u^2) \end{gathered}`

On substituting the known values in the above equation,

`\begin{gathered} W=(1)/(2)*15.0*(11.5^2-7.50^2) \\ =570\text{ J} \end{gathered}`

Final answer:

Thus the total work that must be done on the object to increase its speed to the given rate is 570 J

Therefore the correct answer is option C.