Velocity at Time t: My vs Book Answer

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The initial velocity of a particle is denoted as u, with acceleration given as a function of time, f = at. The correct formula for the velocity at time t is v = u + (at^2)/2, as opposed to the incorrect v = u + at^2. The error arises from misunderstanding that acceleration is time-variant, requiring the use of average acceleration. Participants emphasize the importance of showing work to clarify misunderstandings and suggest using calculus for a more accurate approach. Understanding the distinction between constant and variable acceleration is crucial for solving such problems correctly.
Amith2006
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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?
 
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The book, if you showed your work perhaps, we could point out your error.

~H
 
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
 
Alternatively, Calculus could be used.

~H
 

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