Solve Impulse Problem: Find Lowest Average Force

[ortegavs]

Homework Statement

Which of the following could be accomplished with the least average force?
a: accelerating a 2 kg ball from 0 m/s to 9 m/s in half a second.
b: accelerating a 6 kg ball from 0 m/s to 6 m/s in one second.
c: accelerating a 9 kg ball from 0 m/s to 8 m/s in two seconds.
d: accelerating a 10 kg ball from 0 m/s to 7m/s in two seconds

Homework Equations

F=ma
ma Δt= Δp
p=mv

The Attempt at a Solution

Answer given as correct is D. I used proportions to solve this problem since Δp is proportional to average force. Since initial p is zero for all the problems than Δp is lowest with answer A; pf- pi= 18 kg m/s. If it had asked for force alone than the seconds matter and then you solve for force gives f= Δp/ Δt. If you do it this way a,b, and c all give 36N while d give 35N. But the question does not ask for lowest force it ask for lowest average force. Am I right or did I make a mistake somewhere?

 

[Agent M27]

Ya unfortunately the average force is defined as the Impulse ( or change in momentum) divided by the change in time. I think you were mistaking net force for average force.

Joe

 

[Redbelly98]

I used proportions to solve this problem since Δp is proportional to average force.

... and it's proportional to the time as well. From the impulse equation:

Δp = F_average·Δt​

Δt must be taken into account.