I keep getting -.25. Can someone repeat the calculation? I'm losing my mind here.

Question

The displacement (in meters) of a particle moving in a straight line is given by s = t² − 8t + 15, where t is measured in seconds.

(a) Find the average velocity over each time interval.

[3.5, 4]?

Answer 1

OR...

take the 1st derivative of position to get velocity:

v(t) = s'(t) = 2t - 8

Solve for v(t) at the 2 given points:

v(3.5) = -1

v(4) = 0

average = -0.5

Don't worry about the minus sign---it is an artifact of the process

Answer 2

s(t)= t^2 - 8t + 15 = (t-3)(t-5)

s(3.5) = (.5)(-1.5) = -0.75

s(4) = (1)(-1) = -1

Average Velocity = displacement / time = (-1 - -0.75) / (4 - 3.5) = -0.25 / 0.5 = -0.5 m/s