Question

The linear momentum of a body of mass 8 kg is 24 kg m s$^{-1}$. If a constant force of 24 N acts on the body in the direction of the motion for a time of 3 s, then the increase in the kinetic energy of the body is
Identify the correct option from the following:

• A. 480 J
• B. 540 J
• C. 270 J
• D. 450 J

Hint:

To find the increase in kinetic energy, compute the initial and final velocities using momentum and force, then use $KE = \frac{1}{2} m v^2$.

Answer 1

The Correct Option is B

Step 1: Calculate initial kinetic energy
Mass $m = 8$ kg, momentum $p = 24$ kg m/s. Velocity $v = \frac{p}{m} = \frac{24}{8} = 3$ m/s. Initial kinetic energy $KE_i = \frac{1}{2} m v^2 = \frac{1}{2} \times 8 \times 3^2 = 4 \times 9 = 36$ J. Step 2: Calculate final velocity and kinetic energy
Force $F = 24$ N, time $t = 3$ s. Acceleration $a = \frac{F}{m} = \frac{24}{8} = 3$ m/s$^2$. Final velocity $v_f = v_i + at = 3 + 3 \times 3 = 12$ m/s. Final kinetic energy $KE_f = \frac{1}{2} m v_f^2 = \frac{1}{2} \times 8 \times 12^2 = 4 \times 144 = 576$ J. Step 3: Compute the increase in kinetic energy
Increase in kinetic energy = $KE_f - KE_i = 576 - 36 = 540$ J, matching option (2).