Finding velocity and displacement at any time during uniform acceleration motion

[FaraDazed]

Was not sure whether to post this here on the general forums, as it does kind o relate to coursework, just not directly.

The four equations of uniform accelerated motion. Can you use them to find the velocity and displacement at any specific time by simply just using 't' as the time you are looking for?

My friend has done this on his coursework but I told him I don't think you can use the equations in that manner. I may be wrong(, I'm not totally sure.

Can anyone shed some light on this please?

 

[Doc Al]

The four equations of uniform accelerated motion. Can you use them to find the velocity and displacement at any specific time by simply just using 't' as the time you are looking for?

Why not?

Give an example where you think that wouldn't work.

 

[FaraDazed]

I just assumed that because the equations all involve final velocity they wouldn't work.

Looking at it another way though if in a problem you imagine that the object did stop at the time you were looking for then they would work.

So they do then? I think the above and my classes using calculus to find instantaneous velocities (in variable acceleration) confused me a little!

 

[FaraDazed]

edit: just realized my mistake.

 

[Doc Al]

(I was just replying and I saw your edit.)

 

[Doc Al]

I just assumed that because the equations all involve final velocity they wouldn't work.

Often 'final' velocity just means the velocity at time 't'. And initial velocity means the velocity at time 0.

 

[FaraDazed]

OK, another thing that confused me is finding the displacement of a projectile in motion.

As if a football was kicked or something, not as if something was dropped. As the motion is a parabola, and as displacement is basically the shortest distance from the starting point to the end point, would the displacement from the start to say a third of the way through its motion be found using the equations?

All other problems we have done using constant acceleration have been things like cars moving in straight lines etc, and we have had only had one lesson on projectiles of which none of the problems we were asked to find the displacement at certain parts of the motion.

 

[Doc Al]

As if a football was kicked or something, not as if something was dropped. As the motion is a parabola, and as displacement is basically the shortest distance from the starting point to the end point, would the displacement from the start to say a third of the way through its motion be found using the equations?

Why not?

You could use the equations to find the vertical and horizontal position of the football at any point in time.

 

[FaraDazed]

Why not?

You could use the equations to find the vertical and horizontal position of the football at any point in time.

Right I see, thanks. I was confusing myself and thought it would give the actual displacement at any time rather than the x and y components. Could they then be resolved using Pythagoras to find the actual displacement from the starting point?

If so I assume its the same for the velocity?

 

[Doc Al]

Right I see, thanks. I was confusing myself and thought it would give the actual displacement at any time rather than the x and y components. Could they then be resolved using Pythagoras to find the actual displacement from the starting point?

Of course, if you like.

If so I assume its the same for the velocity?

Sure. You'd solve for the horizontal and vertical components at any time, then combine them to find the total velocity.