Question

A particle of mass m is at rest at t = 0. The force exerting on it in x-direction is F(t) = F e^–bt. Which one of the following graph is of speed V (t) ➙ t

Answer 1

Correct option: (b)

Explanation:

F(t) = F_oe^–bt 

a = (F_o / m)e^–bt 

(dv / dt) = (F_o / m)e^–bt 

integrating

V = (F_o / m) ^t∫_o e^–bt at

V = (F_o / m) [(e^–bt) / (– b)]_o^t 

= (F_o / m) [{e^–bt – 1} / {– b}]

V = {F_o / mb} (1 – e^–bt)

i.e. graph is exponential