Saturday, 28 April 2007

The Equations for Uniform Acceleration

There are four equations for uniform acceleration (also known as the kinematic equations) which are used to describe the motion of an object:

1.
2.
3.
4.

Where:
u – initial velocity
v – final velocity
a – acceleration
t – time
s – displacement


You may be wondering – why there are four equations instead of one? Notice that each equation has one variable missing. For example, the first equation doesn’t have the variable displacement, s, in it. So, if you were to calculate something that involves displacement, equation 1 is not your choice. Basically, if you know any three of u, v, a, t and s, the others can be found using one or more of the above equations. But take note that you can use these equations only when the acceleration of an object is constant throughout its motion.

It’ll be useful to memorize these formulas if you’re going to solve problems involving motion, but do you know how to derive them? Knowing how to derive these formulas is useful because you will understand how these equations originated and this knowledge acts as a backup in case you forgot any one of them – you just have to derive it and they just appear out of nowhere!


Deriving the Equations

Suppose the velocity of a body increases at a consistent rate from u to v in time t, the body is said to be accelerating uniformly and uniform acceleration a is given by


Since the velocity is increasing steadily, the average velocity is the mean of the initial and final velocities:


If s is the displacement of the body in time t, then the average velocity is equal displacement/time or s/t, so we can say


By substituting equation 1 into equation 2, we have


By rearranging equation 1, we know that t = (v-u)/a. We substitute this value of t into equation 2 and we have


There’re other ways of deriving these equations. Can you find them?


See Also

12 comments:

rosaliyo said...

AWESOME DUDE UR BTR TAN MA TEACHER

Anonymous said...

Online solver for these equations http://planetcalc.com/981/

Anonymous said...

thanks soo much, my teacher can't explain in the way i'd like

AAE VIRUS said...

Wow i think am liking this my teacher needs be updated for sure

Anonymous said...

good, straightforward, explanation of the derivation of these equations.
Thanks

Anonymous said...

Definitly made things clearer!
Thanks(:

variemuchechesi said...

thee are excellent explanations for derivation of thee equation.

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Leslie Lim said...

Thanks for sharing your thoughts. I truly appreciate your efforts and I am waiting for your next write ups thanks once again.

Pauleen
www.imarksweb.org

ronan angelo de guzman said...

you really help me in my homework. Thank you very much

Leslie Lim said...

I read your blog.I thought it was great.. Hope you have a great day. God bless.

Rica
www.imarksweb.org

Deepak Suwalka said...

It's a nice approach to uniform acceleration. I really like it. Thanks for sharing it.