How to calculate the average velocity?

In summary, the position of an object moving along the x-axis is given by x = a + bt^2, where a = 8.5m, b = 2.5 ms^-2, and t is measured in seconds. To find the average velocity between t = 2.0 s and t = 4.0 s, calculate the values of x at each time point (x = 18.5 m at t = 2.0 s and x = 40 m at t = 4.0 s) and use the average velocity formula Vavg = (xf - xi)/(tf - ti). After correcting for a mistake, the final average velocity is 15 m/s.
  • #1
Indranil
177
11

Homework Statement


The position of an object moving along the x-axis is given by x=a+bt^2, where a=8.5m,b=2.5 ms^-2, and t is measured in seconds. what is the average velocity between t=2.0 s and t= 4.0 s

Homework Equations


as we know, Vavg = xf-xi / tf-ti (f= final position and time and i= initial position and time)

The Attempt at a Solution


Where to put the values because we have the values of t but there are no values of x
 
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  • #2
Indranil said:
Where to put the values because we have the values of t but there are no values of x
Your problem statement has an equation for x(t) does it not?
 
  • #3
gneill said:
Your problem statement has an equation for x(t) doe it not?
No, the only equation is 'x=a+bt^2'
 
  • #4
average velocity between t=2.0 s and t= 4.0 s
So find x when t=2 and find x when t=4, then you'll have all the data you need.
 
  • #5
Indranil said:
No, the only equation is 'x=a+bt^2'

Yes it does: that IS the expression ##x(t)##---after all, it is telling you the value of ##x## when the time is ##t##!
 
  • #6
Merlin3189 said:
So find x when t=2 and find x when t=4, then you'll have all the data you need.
I am doing this below
x=a +bt^2 =8.5 +2.5 x 4 =18.5 (when t=4)
x=at + bt^2 =8.5 + 2.5 x 2 =13.5 (when t=2)
see the values below
(a=8.5m, b=2.5 ms^-2, t=2.0 s and t= 4.0 s)
Now what to do?
 
  • #7
1- what is average velocity?

2- what do your two x values tell you?
 
  • #8
Merlin3189 said:
1- what is average velocity?

2- what do your two x values tell you?
1. Average velocity = TotalDisplacement / TotalTime
2. The initial position and the final position
If I do the math
Vavg=18.5-13.5 /4-2 = 5/2 (but the answer does not match the answer in my book. in my book, my answer is 15m/s)
Now, what to do?
 
  • #9
Indranil said:
x=a +bt^2 =8.5 +2.5 x 4 =18.5 (when t=4)
x=at + bt^2 =8.5 + 2.5 x 2 =13.5 (when t=2)
see the values below
(a=8.5m, b=2.5 ms^-2, t=2.0 s and t= 4.0 s)
Sorry, I didn't check this before. You forgot to square the time.

Also there is some confusion between, x=a +bt^2 and x=at + bt^2

In the question statement, you gave the first version.

But your last post is correct in your statement of average velocity and working from your previous results. You just need to check those first calculations.
 
  • #10
Merlin3189 said:
Sorry, I didn't check this before. You forgot to square the time.

Also there is some confusion between, x=a +bt^2 and x=at + bt^2

In the question statement, you gave the first version.

But your last post is correct in your statement of average velocity and working from your previous results. You just need to check those first calculations.
It would be x=a+bt^2
 
  • #11
Ok. That's what it said in the Q and it is consistent with the units given for a and b.

So now you can get the right values if you stick to this equation and take care with squaring t.
 
  • #12
Merlin3189 said:
Ok. That's what it said in the Q and it is consistent with the units given for a and b.

So now you can get the right values if you stick to this equation and take care with squaring t.
I did but still, the answer does not match the answer in my book.
As you said I have done below
X=18.5 when t=2 and X=40 when t==4 now according to the average velocity
Vavg=xf-xi / tf-ti = 21.5 /2 ms^-1
 
  • #13
Indranil said:
I did but still, the answer does not match the answer in my book.
As you said I have done below
X=18.5 when t=2 and X=40 when t==4 now according to the average velocity
Vavg=xf-xi / tf-ti = 21.5 /2 ms^-1
Double check your position calculation for t = 4 s.
 
  • #14
gneill said:
Double check your position calculation for t = 4 s.
Thank you for finding my mistake. I checked it and it's done. Now the answer is 15m/s. Thank you all for your kind efforts.
 

Related to How to calculate the average velocity?

1. What is the formula for calculating average velocity?

The formula for average velocity is average velocity = (change in position) / (change in time). This means that you divide the change in position by the change in time to get the average velocity.

2. How do I find the change in position?

The change in position is the final position minus the initial position. For example, if an object starts at position 10 and ends at position 20, the change in position would be 20 - 10 = 10.

3. What units are used for average velocity?

The units for average velocity are distance over time, such as meters per second or kilometers per hour. It is important to use consistent units for both distance and time in order to get an accurate average velocity.

4. Can average velocity be negative?

Yes, average velocity can be negative. This indicates that the object is moving in the opposite direction of the positive direction, or towards the negative direction. For example, if an object moves from position 10 to position 5, its average velocity would be negative because it is moving towards the negative direction.

5. How does average velocity differ from instantaneous velocity?

Average velocity is the overall velocity of an object over a period of time, while instantaneous velocity is the velocity of an object at a specific moment in time. Average velocity takes into account the total change in position and time, while instantaneous velocity only considers a specific point in time.

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