The displacement (in meters) of a particle moving in a straight line is given by s = t^2 − 8t + 19, where t is measured in seconds. Find the average velocity over a time interval [a, b] and the instantaneous velocity at t = 4.

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The displacement of the particle moving in a straight line as a function of time is s = t^2 - 8t + 19.

The average velocity over a time interval [a, b] is:

(b^2 - 8b + 19 - a^2 + 8a - 19)/(b - a)

=> (b^2 - a^2...

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The displacement of the particle moving in a straight line as a function of time is s = t^2 - 8t + 19.

The average velocity over a time interval [a, b] is:

(b^2 - 8b + 19 - a^2 + 8a - 19)/(b - a)

=> (b^2 - a^2 - 8b + 8a)/(b - a)

=> ((b-a)(b +a) - 8(b - a))/(b - a)

=> a + b - 8

The instantaneous velocity at time t is 2t - 8. At t = 4 it is 0 m/s.

The average velocity over an interval [a, b] is a + b - 8 m/s and the instantaneous velocity at t = 4 is 0 m/s.

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