A particle of mass (m ) is at rest at the origin at time (t=0 ) It is subjected to a force, (F(t)=F₀ e^ -b t ) in the (x )-direction. Its speed (v(t) ) is depicted by which of the following curves?

Step-by-step solution

Given ( F ( t )= FO e ^ - bt ), acceleration ( a ( t )= F ( t ) / m =( FO / m ) e ^ - bt ), so (dv/dt=( FO / m ) e ^ - bt ). Integrating with ( v (0)=0 ) gives ( v ( t )=( FO /( mb )) [1- e ^ - bt ] ). This rises from 0 and asymptotically approaches ( FO /( mb ) ). Hence the correct ( v - t ) curve is a rising exponential saturating at ( FO /( mb ) ), which corresponds to (b).