Understanding Velocity and Acceleration Formulas: Common Mistakes to Avoid

[mubashirmansoor]

We all know that the formulae for velocity is v=x/t (x=distance) & that acceleration= (v-u)/t
know as we know x=ut+(at^2)/2 let's replace this value of x in the formulae of velocity & make "a" the subject of furmaulae, What I got was

a=2(v-u)/t istead of a= (v-u)/t Whats my mistake?

 

[AKG]

Your variables don't mean the same things:

Average Velocity = Total Displacement / Elapsed Time
Average Acceleration = (Final Velocity - Initial Velocity) / Elapsed Time
If acceleration is constant: Total Displacement = (Initial Velocity x Time Elapsed) + 0.5[Constant Acceleration x (Time Elapsed)²]

When acceleration is constant, the average acceleration is the (constant) acceleration, so it's okay to use a for both. However, you're using v to denote both the average velocity and the final velocity, and this is where you're getting your problems. What you're getting is:

$$a = \frac{2(v_{avg} - v_{initial})}{t}$$

compared to:

$$a = \frac{v_{final} - v_{initial}}{t}$$

Note that both are correct when acceleration is constant.

 

[mubashirmansoor]

Thanks a lot
The problem is solved