How much net work is required to accelerate a 1200 kg car from 10$ms^{-1}$ to 15$ms^{-1}$

Analysis

To solve this problem, we use the Work-Energy Theorem. This theorem states that the net work done on an object is equal to the change in its kinetic energy.

Concept

The kinetic energy ($K.E.$) of an object is given by the formula:

The net work done ($W$) to change the velocity of an object from an initial velocity ($u$) to a final velocity ($v$) is:

Solution

Given data:

• Mass ($m$) = $1200\text{ kg}$
• Initial velocity ($u$) = $10\text{ ms}^{-1}$
• Final velocity ($v$) = $15\text{ ms}^{-1}$

Step 1: Calculate the change in the square of the velocities.

Step 2: Apply the work formula.

Step 3: Convert to standard form.

Comparing this result to the given options, it matches option C.

Tip

When solving "Work-Energy" problems, always check if you are asked for the total work or the net work. If the question mentions a change in speed, the Work-Energy Theorem is almost always the fastest way to the answer. Avoid calculating acceleration and distance using equations of motion unless absolutely necessary, as it takes much longer and increases the chance of a calculation error!