A car with mass m require 5.0 KJ of work to move from rest to a final spee v. If this sam amount of work is performed during the same amount of time on a car with a mass of 2m, what is the final speed of the second car.

V/2

Since final mV^2 wil be the same for both masses, the larger mass will have velocity v/sqrt2.

2v

To educate

To answer this question, we can use the work-energy principle, which states that the work done on an object is equal to its change in kinetic energy.

Given that a car with mass m requires 5.0 KJ of work to move from rest to a final speed v, we can write this as:

Work = Change in kinetic energy

W = (1/2) * m * v^2

We can rearrange this equation to solve for v:

v = sqrt(2 * W / m) ---- Equation 1

Now, if the same amount of work (5.0 KJ) is performed on a car with a mass of 2m, we need to find the final speed of the second car.

Using equation 1, we substitute the mass 2m and the work 5.0 KJ:

v2 = sqrt(2 * W / (2m))

Simplifying the equation, we have:

v2 = sqrt(W / m)

Therefore, the final speed (v2) of the second car is equal to the square root of the work (5.0 KJ) divided by the mass (m).