Question on velocity at T1 and T2 problem

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In summary, the acceleration of a bus is given by a(t)=at where 1.23 is a constant. Using calculus, we can calculate the velocity of the bus at time = 2.01 to be 2.54 and its position at time = 2.01 to be 10.06.
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Homework Statement



The acceleration of a bus is given by a(t)=at where = 1.23 is a constant.
If the bus's velocity at time = 1.05 is 4.90 , what is its velocity at time = 2.01 ?
If the bus's position at time = 1.05 is 6.09 , what is its position at time = 2.01 ?

Homework Equations



a=v2-v1/t2-t1

The Attempt at a Solution


Tried to use that equation to solve for V2 and got 6.08 as my answer, however masteringphysics said I was incorrect
 
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njt84572 said:
The acceleration of a bus is given by a(t)=at where = 1.23 is a constant.
Something got left out in your cut and paste. Did you mean that a(t) = 1.23t ?
a=v2-v1/t2-t1
That defines average acceleration. Not useful here. (Unless I have guessed wrong about your problem.)

Instead, given the acceleration function how can you calculate a velocity function? Think calculus!
 

1. What is the meaning of velocity at T1 and T2?

Velocity at T1 and T2 refers to the speed and direction of an object at two specific points in time, T1 and T2. It is a measure of how quickly an object's position changes over a certain period of time.

2. How is velocity at T1 and T2 calculated?

Velocity at T1 and T2 can be calculated by dividing the change in position (displacement) by the change in time between T1 and T2. This can be represented by the equation v = (x2 - x1) / (t2 - t1), where v is velocity, x is position, and t is time.

3. What is the difference between velocity at T1 and T2 and average velocity?

Velocity at T1 and T2 is the instantaneous velocity at two specific points in time, while average velocity is the overall velocity over a certain period of time. Average velocity is calculated by dividing the total displacement by the total time.

4. How does acceleration affect velocity at T1 and T2?

Acceleration is the rate of change of velocity, so it can affect the velocity at T1 and T2 by either increasing or decreasing it. If an object is accelerating, its velocity at T1 and T2 will be different from its average velocity.

5. Can velocity at T1 and T2 be negative?

Yes, velocity at T1 and T2 can be negative if the object is moving in the opposite direction of the chosen positive direction. It can also be negative if the object is slowing down or decelerating.

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