Question

The kinetic energies of two similar cars A and B are 100 J and 225 J, respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the ratio F_A/F_B is ______.

Options

• `3/2`

• `2/3`

• `1/3`

• `1/2`

Answer 1

The kinetic energies of two similar cars A and B are 100 J and 225 J, respectively. On applying brakes, car A stops after 1000 m and car B stops after 1500 m. If F_A and F_B are the forces applied by the breaks on cars A and B, respectively, then the ratio F_A/F_B is `bbunderline(2/3)`.

Explanation:

The work done by the braking force (F) in stopping the car over a distance (s) is equal to the change in its kinetic energy (K).

W = ΔK

F.s = K

Since `F = K/s`, we can compare the two cars by taking the ratio of their forces:

`(F_A)/(F_B) = ((K_A)/(K_B))((s_B)/(s_A))`

= `100/225 xx 1500/1000`

= `150/225`

= `2/3`