What is the average speed of a particle with given position and time data?

[Casimi]

Homework Statement

The position of a particle as a function of time is given by x = (-5.06 m/s)t + (3.05 m/s2)t2. Calculate the average velocity of the particle from t = 0 to t = 1.20 s.
-1.40 m/s (this is correct, from my calculations)

2nd part: Calculate the average speed from t = 0 to t = 1.20 s

The Attempt at a Solution

I have tried this for hours and cannot arrive at the correct answer for the second part. I tried taking the total distance and dividing by the total time. Could someone please point me in the right direction to find average speed? I have even tried differentiation.

Any assistance would be appreciated. Thanks!

 

[madah12]

you can differentiate to get the velocity then take the integral of its absolute value then divide it by time

 

[Casimi]

I tried that but I am still not arriving at the correct answer. I arrive at a number far larger than it should be.

I cannot figure out what I am doing wrong.

 

[madah12]

did you make sure to separate it into two integral when you integrated the absolute value one negative and one positive?

 

[Casimi]

(-5.06+6.10t) - that is my answer after differentiating. Integrating the absolute value, I have 5.06t+3.05t^2 with integral limits of 0 to 1.20. When I put the values in the integral, I get 9.456 and when divided by 1.2, I get 7.88 which is not the correct answer.

 

[madah12]

I am saying as integral the absolute value
you must know if when v = 0 lies in your interval
-5.06+6.10t=0
t=5.06/6.10 this lies in the interval so you make the integral negative here and positive from it to 1.2

 

[Casimi]

Yes, I tried that and am still not arriving at the right answer. 5.06/6.10 will give .82. If I integrate from -5.06t+3.05t^2 [0 to .82] + 5.06t+3.05t^2 [.82 to 1.2] I am still going to get :
5.06t +3.05t^2 [0 to 1.2]? Please help me out.

 

[madah12]

what you do is get the integral from 0 to .82 (5.06-6.1t)dt
+ the integral from .82 to 1.2 (-5.06 +6.1t)dt

 

[Casimi]

I came up with 2.51m/s but it is still showing as incorrect. Is this the solution that you arrived at?

 

[madah12]

did you divide it by the time?

 

[Casimi]

Thank you! You just saved my grade!