Understanding Velocity, Acceleration, and Equations

[The_Z_Factor]

This doesn't involve a problem, but I am confused on another part involving velocities and acceleration and such..

My book gives me 4 equations, the first one is:
final Velocity=initial Velocity + (acceleration)(time)

The second one:
distance traveled=(intial Velocity + final Velocity)/2

The third:
distance traveled=(intial Velocity)(time)+1/2(acceleration)(time)squared

And the final:
final Velocity squared=(initial Velocity)squared+2(acceleration)(distance)


My question is, under what circumstances are each equation used? My book gives several problems but it uses all of these without really explaining how to use each one, or under which scenario we use each one..like for example, if I want to find the time it takes to go x distance, traveling at s velocity and accelerating at a, then which one would I use?

 

[qspeechc]

For the example you gave, then you would use the third equation.
It would be a good idea to set out your work like this:

First write down all the quantities you are given, or can deduce, with their values. Then write down all the quantities you want to find. Now you must look for the relevant equation. Look at all the things you know AND the thing you want to find. Find the equation that relates all the quantities you know AND want. This will be the equation you must use. You may need to re-arrange the equate so that you can get the quantity you want.

 

[malty]

This doesn't involve a problem, but I am confused on another part involving velocities and acceleration and such..

My book gives me 4 equations, the first one is:
final Velocity=initial Velocity + (acceleration)(time)

The second one:
distance traveled=(intial Velocity + final Velocity)/2

The third:
distance traveled=(intial Velocity)(time)+1/2(acceleration)(time)squared

And the final:
final Velocity squared=(initial Velocity)squared+2(acceleration)(distance)


My question is, under what circumstances are each equation used? My book gives several problems but it uses all of these without really explaining how to use each one, or under which scenario we use each one..like for example, if I want to find the time it takes to go x distance, traveling at s velocity and accelerating at a, then which one would I use?

All these equations are valid only for uniform acceleration. So if you have a car travels at 100mph one second 101 the next, and 104 the next, then it isn't uniforming accelerating so you cannot use the above equations.
If however the car was traveling for 0 to 100m/s^2 and accelerated uniformly at 2m/s^2 then you could use the above equations.

To put it simply if the acceleration when plotted versus times is a curve the equations can't be used. If the acceleration versus time is a straight line then the equations can be used.

 

[The_Z_Factor]

gspeechc, thanks for that advice, I am sure itll probably help me. Malty, thanks for your input as well, I am just starting on the changing velocities or I guess as you said when the acceleration versus time is curved.

 

[Saladsamurai]

You need to take into acount what it is that you are looking for and what variables you are given. If you plug the given information into an equation and what are you are looking for is the only unknown left in the equation, I would say you have chosen wisely.

Casey