Quick Physics Question.?

Question

I'm a junior in high school... in AP Physics.

Just a quick question: what is the difference between the equation:

(Final Velocity Squared) - (Initial Velocity Squared) = 2ad

and the equation:

(Final Velocity) = (Initial Velocity) + at

What i'm trying to find out is if a projectile is shot off a cliff, what is its final vertical velocity before it hits the ground. If i know the acceleration, time, initial velocity, and even distance, and i want to find final velocity... then why can't I use either equation. He wants us to use V=Vo+at... but I argue that I can also use Vf² - Vi² = 2ad.

Answer 1

There are five  quantites involved in the equations of motion.

V0 – initial velocity

V – the final velocity.

a – accelearation

t – time of motion.

d – the distance traveled.

The basic equations are:

a = {V – V0} / t. and

d = {V + V0}*t / 2. Average velocity x time

From these eqations we derive the following  five equations.

1. V = V0 + at which is the same as a = {V – V0} / t

2. d = {V + V0}*t / 2. Average velocity x time

3. d = V0 *t + ½ a t^2

4. d = V*t – ½ at^2.

5. V² - V0² = 2ad

In each equations there are four  among the five quantities( V, V0, a , d and t).

In the first equation V = V0 + at, there is no “d”.

In the 2nd equation d = {V + V0}*t / 2 there is no “a”.

In the 3rd equation d = d = V0 *t + ½ a t^2 there is no “V”.

In the 4th equation d V*t – ½ at^2.there is no “V0”.

In the 5th equation. V² - V0² = 2ad  there is no “t”.

One can use any equation depending upon the problem.

But we must remember that the quantity which is absent in an equation cannot be found using that equation.

We cannot find d using equation 1.

We cannot find a using equation 2.

We cannot find V using equation 3

We cannot find V0 using equation 4

We cannot find t using equation 5

Answer 2

Use whichever eq contains the given variables of the problem.  When t is not given, V² - Vo² = 2ax may be the only rational way to go.

Answer 3

The difference is that the first equation does not depend on time, but on distance.

The second equation does not depend on distance, it depends on time.

If you have distance, acceleration, initial velocity, and time, then you can use either equation.  

The reason to have two equations is in case you don't have one of those pieces of information- if you have everything, use whatever you want and you'll get the same answer.

Hope this helps