EK Physics question

[05med05]

Hi, I posted this under physics questions, but hadn't heard back earlier today.

This is probably trivial, but I can't seem to grasp it.

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Can someone explain to me the difference between the following linear motion / constant accelleration equations:

X = Xi + Vit + (1/2)at(squared)

and

Vf = Vi + at


This is from a question in the 1001 physics book (I think the q # is 293?). Anyway, the question is asking to find initial velocity (Vi) and the explanation in the back instructed me to use the first equation, since x,a and t were known (or could be figured out). The question asked for the initial maximum velocity required of a ball being thrown upwards by a person riding up 6 floors in an elevator. The person throws the ball up when the elevator starts moving and catches it whern the elevator stops on the 6th floor 25m up.

The answer was Vi = 52.5m/s (the answer choice listed 55m/s as the correct option).

Using the equations, if t = 10 seconds and a=gravitational force, then:

If Vf and Xi are zero, then why is there a difference between the first and second equation and when should one be used and not the other and vice versa?

Vf=Vi + at
0=vi + (-10) (10)
Vi = 100m/s

X=Xi + vit + 1/2 at squared
25=0 + Vi(10) + 1/2 (-10) (10) squared
Vi = (25 - (1/2) (-10) (100)) / 10
Vi = 52.5 m/s

Any takers??

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[Sicilian]

I used just one equation to solve the problem:

y = Vot + (1/2)(a)(t^2)

I chose up to be positive. Rearranging the above equation:

Vo = y - 1/2(a)(t^2) / (t)

= ((25 - (1/2)(-10)(100))/(10)

= 52.5 m/s

To answer your other question: Vf = Vo + at could not be used in this problem, since you don't know Vf. Generally speaking, you can use both equations in any problem involving initial/final velocity, displacement, acceleration, and time. If I remember right, y = Vot + 1/2(a)(t^2) actually describes the motion of a falling object. Of course, that does not imply the object is falling, as this problem shows. Its not necessary to take an equation at face-value; you can always rearrange it.

 

[Mister Pie]

Vf is not zero! Don't worry though, it's a fairly common mistake (and one I ocassionally revert back to myself). Remember, right before striking the ground, there IS velocity. The reason people tend to think that vf = 0 is because they consider AFTER the object has struck the ground, at which point an external force has been exerted (so acceleration isn't only due to gravity).