A constant force acts on a body of mass 50kg and changes its speed from 20$ms^{-1}$ to 90$ms^{-1}$ in 10 seconds. Calculate the magnitude of the force applied.

Analyze the question: A constant force changes the speed of a 50 kg body from 20 m/s to 90 m/s in 10 s. We need the magnitude of the force.

Concept: Newton's second law says force equals mass times acceleration, and acceleration is the change in velocity divided by time.

F = ma, where a = (v − u) / t

(Equivalently, F = change in momentum / time.)

Solution:

• Mass, m = 50 kg
• Initial speed, u = 20 m/s
• Final speed, v = 90 m/s
• Time, t = 10 s

Acceleration: a = (90 − 20) / 10 = 70 / 10 = 7 m/s²

Force: F = ma = 50 × 7 = 350 N

Check using momentum: Change in momentum = 50(90 − 20) = 3500 kg·m/s F = 3500 / 10 = 350 N ✓

Answer: The force is 350 N, which is option D.

Tip: When a question gives two speeds and a time, find the acceleration first, using (v − u)/t. Then multiply by the mass. Always subtract the initial speed from the final speed. A common mistake is using 90 − 20 incorrectly or forgetting to divide by time, which would give 3500 N, a value not among the options.