A particle of mass m is at rest at the origin at time t =0 . It is subjected to a force F ( t )= F ₀ e ^ - bt in the x direction. Its speed v(t) is depicted by which of the following curves?

Step-by-step solution

F = F ₀ e ^ - bt a = F m = F ₀ ~m e ^ - bt dv dt = F ₀ ~m e ^ - bt dv = ₀^ t F m e ^ - bt dt v= F m [ -1 b ] [e^ -b t ]₀^t v= F m b [e^ -b t ]v=0 at t=0 and v F m b as t So, velocity increases continuously and attains a maximum value of v= F m b as t .