Aparticle of mass m moves along a straight line with initial speed vi. a force of magnitude f pushes the particle a distance d along the direction of its motion.

part a: find vf, the final speed of the particle after it has traveled a distance d. express the final speed in terms of vi, m, f, and d.

part b: by what multiplicative factor rk does the initial kinetic energy increase, and by what multiplicative factor rw does the work done by the force increase (with respect to the case when the particle had a mass m)? if one of the quantities doubles, for instance, it would increase by a factor of 2. if a quantity stays the same, then the multiplicative factor would be 1. you should enter the two factors separated by a comma.

part c: the particle's change in speed over the distance d will be the change in speed when it had a mass equal to m.

part d: by what factor rk does the initial kinetic energy increase (with respect to the first situation, with mass m and speed vi), and by what factor rw does the work done by the force increase? again, enter the two factors, separated by a comma.