A student decides to compute the velocity at t = 0.8 using algebraic methods. Th

Question

A student decides to compute the velocity at t = 0.8 using algebraic methods. The student begins with the correct formula but proceeds incorrectly, as shown below (picture).

As mentioned in the picture, please explain in two sentences or less what was done wrong. Thanks!

h 2-3.125u2 The correct expression: u-0.8 3.125 u2 0.64) u 0.8 3.125(u-0.8)( u + 0.8) 3.125(u0.8) (u0.8) is factored: :- As u 0.8 and simplified: =-3.125(u + 0.8) dh then evaluated at u - 0: =-3.125(0 + 0.8) =-2.5 m/s dt It=0.8 In two sentences or less, explain what the student did wrong.

Explanation / Answer

All the work was correct but this was clearly the student trying to find the average velocity over a particular time interval....

So, the student erred in plugging in u = 0. Clearly here the time interval is like on the interval [0.8, u] or [u , 0.8].

When you plug in u with 0, the student fails to realize that the time interval, u must be a value extremely close to 0.8 if u wanna get the instantaneous velocity at t = 0.8

So, here's the ans :
The student erred in plugging in u = 0 because a time interval of [0 , 0.8] is way too far apart to be able to get a good read on the instantaneous velocity of the object at t = 0.8. The student must substitute a value much closer to 0.8 to try and get the instantaneous velocity

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