Answer to Question #3803 in Mechanics | Relativity for Vikas

Question

A force is applied on a body mass 50 kg for 8 sec. After that force is removed, but the body continuous in motion for 5 sec and covers 80m displacement. Find the force applied.

Answer 1

Let's denote the force as F.
If 80 m is the distance that the body covers after 8 sec, we can find the the constant velocity :
V = S/t2 = 80/5 = 16 m/s.
V = at₁ = F/m *t = F/ 50 * 8 = 16 m/s
F = 100 N

If 80 m is the total distance covered by the body:
The acceleration whould be a = F/m = F/50, the velocity after 8 sec is V = at = F/50 * 8 = 4F/25 m/s.
The distance after 8 sec is D = at²/2 = F/50 * 64 / 2 = 16F/25 m.
Then the body is moving for 5 sec with constant velocity: S = Vt = 4F/25 *5 = 4F/5 m.
The total distance is 80 m:
16F/25 + 4F/5 = 80
(16 + 20) F/ 25 = 80
F = 80*25/36 = 55 5/9 = 55.56 N