A particle moves on a line away from its initial position so that after t hours it is s = 2t^2 +3t miles from its initial position.

Question

Find the average velocity of the particle over the interval [1, 4]. Include units in your answer.

 

Thank you!!

Answer 1

Actually you would want to use the Physics definition of average velocity.  Physics states that average velocity is the change is position over the change in time. 

 

You don't have to derive or integrate to find the answer to this problem.  Derivation is necessary if you were to find the instantaneous velocity.  We are not finding instantaneous velocity therefore no derivation is necessary. 

 

Using the physics definition of Average velocity, you would do a (f(4)-f(1))/3

 

f(4) = 2(16)+6 = 38

f(1)= 2(1)+3

 

38-5=33.  Divide this by the change in time which is 3.  Your answer should be 11. Thanks!

Answer 2

Velocity is the first derivative of position. Acceleration is the second derivative of position or the first derivative of velocity. Keep these ideas in mind when solving these types of problems.

 

After you calculate the derivative of F(t) using the upper(4) and lower(1) limits remember to subtract.

 

I calculated 12 miles per hour using that process.

 

Please recall that the derivative with respect to t of (2t^2 + 3t) is 4t + 3     (19 - 7 = 12)

Answer 3

To find the average velocity, take the integral of s between t=1 and t=4.  That is

 

F(4) - F(1)

 

where         F(t) = ∫(2t² + 3t)dt