Question #3803

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.

Expert's answer

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 = at_{1 }= 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 = at^{2}/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

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 = at

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 = at

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

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