Question

A mass m is at rest on a horizontal frictionless surface at t=0. Then a constant force F₀ acts on it for a time t₀. Suddenly the force doubles to 2F₀ and remains constant until t=2t₀.

Determine the total distance traveled from t=0 to t=2t_0, in terms of the variables m, F₀, t₀, and appropriate constants.

Answer 1

here,

since, F = mass * acceleration
for t= to
a = F0 / m ----------------------------(1)

by using second equation of motion we have,

S = Vi*t + 0.5*a*t^2 ----------------------------(2)
so,

S1 = 0.5 * ( F0 / m)*t0^2 ---------------(3)

When,

F = 2F0
t = 2t0
Eqn 1 can be written as
a = 2F0 / m ----------------------------(4)

Therefore Eqn 2 can be written as

S2 = 0 + 0.5 * ( 2F0 / m)*4t0^2

S2 = 8 ( 0.5 * ( F0 / m)*t0^2 )
or
S2 = 8*S1

Total Distance Travelled will be Equal to

S = S1 +S2 = S1 + 8S1 = 9S1
Using Eqn 3 we get

S = 9*( 0.5 * ( F0 / m)*t0^2 )

S= 4.5*( F0 / m)*t0^2