Finding time taken to stop a skater given mass, velocity and force

[Anmol Dubey]

Homework Statement

An ice skater with a mass of 60 kg moves with a constant speed of 8 m/s in a straight line. How long
will it take a force of 120 N to stop the skater if it were applied so as to oppose the motion? What would
the speed of the skater be if the force were applied for twice as long?

Relevant Equations

p=mv
kinetic energy = 1/2mv^2

I derived the formula for t but don't know how it works
Δt = p/F

I got
p = mv
= 60*8
= 480kgms^-1

Δt = 480/120N
= 4s

Is that correct?

 

[PeroK]

You could check your answer by using $F = ma$.

 

[Anmol Dubey]

You could check your answer by using $F = ma$.

Oh so a = v/t
= 8/4 = 2m/s² (?)
F = ma
= 60*2 = 120N

 

[PeroK]

Oh so a = v/t
= 8/4 = 2m/s² (?)
F = ma
= 60*2 = 120N

That's not a complete answer. And, it doesn't take into account that the force is opposite to the motion. Neither did your original solution.

You should start the solution by deciding which direction is positive. It would make sense to me that the skater's initial velocity (and momentum) are positive. I.e. $v_0 = +8 \ m/s$. This means that the force is $F = -120 \ N$.