A body initially at rest undergoes rectilinear motion. The forcetime (F-t) graph for the motion of the body is given below. Find the linear momentum gained by the body in 2 ~s .

Step-by-step solution

The impulse J delivered to a body is equal to the change in its linear momentum p . The impulse is given by the area under the force-time ( F-t ) graph. For the interval t = 0 to t = 2 s, the graph represents a semi-circle below the time axis with radius r = 1 s and amplitude A = 4 N. The area of this semi-circle is A_ area = 1 2 r^2 . Since the area is below the time axis, the impulse is negative: J = - 1 2 (1)^2 = - 2 N-s. The magnitude of the linear momentum gained is |J| = | - 2 | = 2 N-s. Answer: 2 ~N - s