The graph below shows the variation of a force F with time t on a body which is moving in a straight line. Dependence of force on time is F ∝ t n . Initially body is at rest. If the speed of the object is 2 m / s at 3 s , then the speed at 4 s will be approximately (in m / s )

Step-by-step solution

Given force varies as F ∝ t n ⇒ F = k t n . . . . i From graph, we observe at t = 2 s , F = 2 N and at t = 4 s , F = 16 N So, putting the values in Eq (i), we have 16 = k 4 n and 2 = k 2 n ⇒ 8 = 2 2 n 2 n ⇒ n = 3 Also, 2 = k 2 n ⇒ 2 = k 2 3 ⇒ k = 1 4 So, force is given by F = t 3 4 Now, F = d p d t , (where, p = momentum) ⇒ d p = F d t ⇒ ∫ v i v f d p = ∫ t i t f F d t ⇒ m v f - v i = ∫ t i t f t 3 4 · d t ⇒ m v f - v i = t f 4 - t i 4 16 . . . . ii Now, when t i = 0 and t f = 3 s We have, v i = 0 and v f = 2 ms -