Calculate average speed/acceleration for the given function

In summary, the conversation is discussing a problem from Serway Physics Chapter 2 that involves an object moving along the x-axis according to a given equation. The problem asks for the average and instantaneous speed and acceleration at various time intervals, as well as the time at which the object is at rest. The solution involves calculating average velocity and applying equations to find the requested values.
  • #1
Alexanddros81
177
4

Homework Statement


Serway Physics Chapter 2

20. An object moves along the x-axis according to the equation ##x=3.00t^2 - 2.00t+3.00##,
where x is in meters and t is in seconds. Determine (a) the average speed between
t=2.00s and t=3.00s, (b) the instantaneous speed at t = 2.00s and at t=3.00s, (c) the average acceleration
between t=2.00s and t=3.00s and (d) the instantaneous acceleration at t=2.00s and t=3.00s.
(e) At what time is the object at rest?

Homework Equations

The Attempt at a Solution



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[/B]
In part (a) I calculated average velocity but it asks for the average speed which is
given by ##v_{avg} = \frac {d} {Δt}## where d is distance traveled between 2 and 3 seconds, which is
13m. So average speed is the same as average velocity in this case.

Is the above correct?
 

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  • #2
It all looks ok.
 

Related to Calculate average speed/acceleration for the given function

1. How do I calculate average speed/acceleration for a given function?

To calculate average speed, divide the total distance traveled by the total time taken. To calculate average acceleration, divide the change in velocity by the change in time. Both of these calculations require the given function to be in terms of distance and time.

2. What is the formula for average speed/acceleration?

The formula for average speed is distance divided by time. The formula for average acceleration is change in velocity divided by change in time.

3. Can average speed/acceleration be negative?

Yes, average speed/acceleration can be negative if the object is moving in the opposite direction than the positive direction established in the function. This indicates that the object is slowing down or moving in the negative direction.

4. How do I interpret the average speed/acceleration value?

The average speed value represents the average rate at which the object is moving over a given distance and time. The average acceleration value represents the average rate at which the object's velocity is changing over a given time period.

5. Can I calculate average speed/acceleration for a non-linear function?

Yes, you can still calculate average speed/acceleration for a non-linear function. However, the calculations will be more complex and may require calculus. It is important to make sure the function is in terms of distance and time before attempting to calculate average speed/acceleration.

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