What's this formula?

Question

v^2 = u^2 + 2as ?

This formula is used for what? I was looking through the book just now when I came across this formula that I have never seen before...Please help me by telling how to use this formula and when to use this formula...What's impt is that you can tell me how do you derive this formula cos I HAVE NEVER SEEN IT BEFORE? Thanks

Answer 1

It is an equation of motion.

v = final velocity
u = initial velocity
a = rate of acceleration
s = distance traveled.

Given any three, the fourth can be calculated.

For example, suppose when a car accelerates from 2 m/s to 12 m/s it traveled 30 m. Calculate its rate of acceleration, assuming it is constant.

u = 2 m/s
v = 12 m/s
s = 30 m

making 'a' the subject of the formula, a = (v^2 - u^2)/2 s.

In vertical motion, two things should be kept in mind:

For upward motion, the final velocity, v = 0 (at the highest point), and a = -g, that is -9.81 m/s^2.

For downward vertical motion (as when a small lead ball is dropped), the initial velocity, u, = 0 and a = +g, that is 9.81 m/s^2.

In all of these examples, air resistance is ignored.

Sorry, I don't have the time to show how the formula is derived. I hope someone else does that.