Velocity at Time t: My vs Book Answer

[Amith2006]

Sir,
The initial velocity of the particle is u (at t=0) and the acceleration f is given by at. What is the velocity of the particle at a time t?
My answer is v = u + at^2 but the book answer is v = u + (at^2)/2. Which is right?

 

[Hootenanny]

The book, if you showed your work perhaps, we could point out your error.

~H

 

[arunbg]

As Hoot stated, the book is right. Perhaps Amith, you are directly substituting the value of acceleration directly into v = u + at
But in this case acceleration is not constant but time variant (linearly).
So you need to take average acceleration which is ...

And please show your working or thoughts. I have often noticed in your earlier posts that you seldom show any working at all . We don't do other people's homework, we merely help.

Arun

 

[Hootenanny]

Alternatively, Calculus could be used.

~H