# Homework Help: Impulse problem

1. Jul 10, 2010

### ortegavs

1. The problem statement, all variables and given/known data
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

2. Relevant equations
F=ma
ma Δt= Δp
p=mv

3. The attempt at a solutionAnswer 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?

2. Jul 10, 2010

### 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

3. Jul 11, 2010

### Redbelly98

Staff Emeritus
... and it's proportional to the time as well. From the impulse equation:
Δp = Faverage·Δt​
Δt must be taken into account.