Calculating velocity, given mass and force

[dinhjeffrey]

Homework Statement

[URL]http://img705.imageshack.us/i/10001c.jpg/[/URL]
http://img705.imageshack.us/i/10001c.jpg/

Homework Equations

F=ma
a=v/t

The Attempt at a Solution

the answer is C) 3m/s but I am not too sure how to get there.
this is what I've attempted.
t= [1,2] - average force is (2N - 0)/(2-1 seconds) = 2N
t=[2,4] - 2N / 2seconds = 1N
t= [4,5] - -2N/1second = -2N
so adding all the forces together i get 2+1-2 = 1N
F=ma
1 = 2a
a=1/2
a=v/t
1/2 * 5seconds = v
v= 2.5 <-- but clearly it is wrong

 

[da_nang]

t= [1,2] - average force is (2N - 0)/(2-1 seconds) = 2N
t=[2,4] - 2N / 2seconds = 1N
t= [4,5] - -2N/1second = -2N

Your dividing force by second which does not equal force. Since the force also changes in two intervals means that the acceleration also changes, which makes going through Newton's second law a bit more messier.

On the other hand, there's an easier way because the velocity of the object changes only when acted by the force. When the force F(t) acts on the object for a time t, it creates an impulse. The impulse results in a change of the momentum of the object.

 

[dinhjeffrey]

Your dividing force by second which does not equal force. Since the force also changes in two intervals means that the acceleration also changes, which makes going through Newton's second law a bit more messier.

On the other hand, there's an easier way because the velocity of the object changes only when acted by the force. When the force F(t) acts on the object for a time t, it creates an impulse. The impulse results in a change of the momentum of the object.

oh i get that divding the force by time is wrong but i do not get your second paragraph. can you explain it more noob-friendly? =3

 

[ojs]

You are calculating the average force incorrectly when it is changing (that is in the [1,2] and [4,5] intervals).
Also when the force is constant, what does that tell you about the acceleration?
If you know the acceleration you can figure out the increase in velocity can't you?

 

[dinhjeffrey]

You are calculating the average force incorrectly when it is changing (that is in the [1,2] and [4,5] intervals).
Also when the force is constant, what does that tell you about the acceleration?
If you know the acceleration you can figure out the increase in velocity can't you?

i don't get to find force from [1,2] and [4,5]
actually i think i got more confused now ><
do i have to find the total acceleration then plug it into v= v(i) + at?
or does acceleration = increase in velocity?
is increase in velocity mean the rate of change of velocity or the difference between the final velocity and initial velocity?

 

[ojs]

Ok, first thing first.
You do realize that acceleration is a change in velocity, so that when you have an acceleration of 1 m/s^2 that means the velocity changes 1 m/s for every second that passes.
Lets then start with the easy bit, the time from 2 to 4 seconds since the force is constant there. What is the acceleration during that period?

 

[dinhjeffrey]

Ok, first thing first.
You do realize that acceleration is a change in velocity, so that when you have an acceleration of 1 m/s^2 that means the velocity changes 1 m/s for every second that passes.
Lets then start with the easy bit, the time from 2 to 4 seconds since the force is constant there. What is the acceleration during that period?

F= ma, so Force is 2
mass is 2kg, (given)
plug in equation
2= 2a
a=1 right?

 

[ojs]

correct, so what is the velocity increase during that period?

 

[dinhjeffrey]

v/t = a
so v/2seconds = 1
v = 2 m/s ?

 

[ojs]

correct, so now we know how much the velocity increased during those two seconds.
The periods [1,2] and [4,5] are identical so we only need to focus on one of them, let's use the first one.
What is the average force during the period [1,2] (and it is not 2N, that is the maximum force, the average is always lower then the maximum).

 

[dinhjeffrey]

would average force be 1 since its in the middle? o.o

 

[ojs]

yes, and besides it being in the middle you also need to use the fact that the force line is a straight line there, had it not been straight you could not have known so easily that the average force was 1N (try to use correct units when posting, it helps you understand what is going on).
So what is the average acceleration during that period and then the average velocity increase? Multiply by two (to include the [4,5] period), add the 2 m/s we got earlier and you have your result.

 

[dinhjeffrey]

yes, and besides it being in the middle you also need to use the fact that the force line is a straight line there, had it not been straight you could not have known so easily that the average force was 1N (try to use correct units when posting, it helps you understand what is going on).
So what is the average acceleration during that period and then the average velocity increase? Multiply by two (to include the [4,5] period), add the 2 m/s we got earlier and you have your result.

ohh okay got it thanksss!