Finding net force using velocity graph?

[jennaskim]

Finding net force using velocity graph?

The figure(Figure 1) shows the velocity graph of a 2.5object as it moves along the x-axis.

What is the net force acting on this object at t=7 ?



The attempt at a solution

Since F=ma, I tried first finding a by dividing 6 m by 7 s. Then I got 0.857 m/s² x 2.5 kg = 2.1429 ≈ 2.1 ...but it's wrong :(

Please help.

 

[rude man]

What you need to do is plot acceleration on the same graph. Acceleration = a_x*dv_x/dt. So at first the particle accelerates positively a certain amount (how much?), then stops accelerating, then accelerates negatively another certain amount (again, how much?).

Now, keeping in mind F_x = ma_x, read off a_x on your newly created chart and use this formula.

What comment might you have regarding the a_x graph for x < 6 s?

 

[jennaskim]

I got a= -2 at t = 7.
I did F = 2.5 x 2 = 5.0 ...It's still wrong

 

[rude man]

I got a= -2 at t = 7.
I did F = 2.5 x 2 = 5.0 ...It's still wrong

How did you get a = -2 at t = 7? That's really off.

 

[jennaskim]

Nevermind. I think it's a = 6? I took the slope = 12 / 2 = 6

 

[jennaskim]

correction: -6 ?

 

[jennaskim]

I used a = -6, and i got the right answer! Thanks for you help

 

[Cbray]

Force is a change in momentum, the momentum changes for the first 3s and the last 2s - The force is constant since the decrease in velocity is linear. Find the change in velocity over the period of time when you know the momentum is changing, then you get the force. You know this is exact since the change in velocity throughout each time period is constant (not changing) - i.e. it is not an approximation.