Question

A certain amount of work W is required to accelerate a car from rest to a speed v. If instead an amount of work equal to 2W is done on the car, what is the car's speed?​

Answer 1

Given,

When W amount of work is given the car accelerates from rest to a speed of Vm/s.

To Find,

What will be the car's speed when work done of 2W is applied on the car?

Solution,

We know that " When a force applied on a body and the body gets displaced by a certain distance, work done is produced".

So,  W = F×S

Where F = force

           S = displacement

⇒ W = m×a×S   [∵ F = ma ]

⇒ W = m×$\frac{v}{t}$×S    [∵ a = $\frac{v}{t}$ ]

Where m = mass of the car

          a = acceleration

          v = speed or velocity

          t = time

From the above equation we can see that,

Workdone is directly proportional to speed.

⇒ W ∝ V

So, when the work done will be doubled to 2W then speed will be doubled to 2V m/s.

Hence, when work done equal to 2W is done on the car, the car's speed will be doubled that is 2V m/s.