# Force v time

If a force v time graph made a sine curve, then the acceleration v time would create a sine curve too correct? However, the velocity v time curve would look like a pi/2 shift to the right? Are these thoughts correct?

## Answers and Replies

yes going from acceleration to velocity can be done by integrating the sine. This yields a cosine (with minus sign in front of it) and as you know sin(x) = cos(90°-x)...

marlon

when is force negative?

And why is force v time and acceleration v time the same curve?

when the force vector points in the opposite direction of the x-axis for example.

The magnitude of a force is never negative in classical physics...
The minus sign has to do with orientation along some give axis.

marlon

The time dependent curve is the same for force and acceleration because F=ma. So basically the only difference is the mass, which is constant during the entire motion.

marlon

I'm starting to understand, but I'm still a little iffy on the negative force. Say a cart moves towards the origin slowing down and at a steady rate, it turns around after 2 seconds and then moves away from the origin speeding up at the same steady rate. The v vs t graph would look like a steady positive slope from negative to positive where x=0 at 2 seconds...what would force look like?

when the acceleration vector is positive, it means you go faster and faster. When it is negative you are slowing down. Same thing for the force-vector since it is the acceleration vector multiplied by a positive constant (the mass)

marlon

ohhh, so the force vs time is the same as the acceleration vs time graph?! because mass is always constant!

yes it is...
marlon

what about a force vs acceleration graph? It would just be a straight line?

well yes if a is one definite value.
You can also plot the force v a for different a values, then you would get a straight line through the origin.

marlon

when two equal forces are applied to an object...one form the left and the other from the right...the object is kept stationary, however, the new force would be the combination of both forces from the left and right correct?