Velocity at Time t: My vs Book Answer

Arum summarized the conversation stating that the book answer is correct in the given scenario and that Amith may have made a mistake by substituting the value of acceleration directly into the formula. Arum also suggests showing working or thoughts to receive better help and mentions that Calculus could also be used. In summary, Arum states that the book answer is v = u + (at^2)/2 and suggests showing working or using Calculus for better understanding.
  • #1
Amith2006
427
2
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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  • #2
The book, if you showed your work perhaps, we could point out your error.

~H
 
  • #3
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
 
  • #4
Alternatively, Calculus could be used.

~H
 

FAQ: Velocity at Time t: My vs Book Answer

What is velocity at time t?

Velocity at time t refers to the measurement of an object's speed and direction at a specific moment in time. It is typically represented in units of distance per time, such as meters per second.

How is velocity at time t calculated?

Velocity at time t can be calculated by dividing the change in position of an object by the change in time. This is represented by the formula v = (xf - xi) / (tf - ti), where v is velocity, xf and xi are the final and initial positions of the object, and tf and ti are the final and initial times.

What factors can affect velocity at time t?

Velocity at time t can be affected by various factors, such as acceleration, force, friction, and air resistance. These factors can either increase or decrease the velocity of an object at a specific moment in time.

How is velocity at time t different from average velocity?

Velocity at time t represents the instantaneous speed and direction of an object, while average velocity represents the average speed and direction of an object over a period of time. Average velocity takes into account the change in position and time, while velocity at time t only considers the velocity at a specific moment.

Why is velocity at time t important in physics?

Velocity at time t is important in physics because it helps us to understand the motion of objects and how they change over time. It is a key concept in kinematics and is used to calculate other important quantities such as acceleration and displacement.

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