The position of an object moving along a line is given by the function s left parenthesis t right parenthesis equals negative 20 t squared plus 120 t

Question

Find the average velocity of the object over the following intervals.

a. [1,4]

b. [1,3]

c. [1,2]

d. [1,1+h] where h>0 is any real number

a.​ The average velocity of the object over the interval​ [1, 4] is _..... and etc.

Answer 1

The usual calculation of average velocity in calculus class is to take the integral of v(t) for a time interval and then divide by the time interval. However, in this case you need only evaluate the position at the end of the interval and subtract the position at the beginning of the interval and then divide by the time interval.

a) v average for interval [1,4] = s(4) - s(1) / (4 - 1) = 60 m/ 3 s = 20 m/s

The rest is up to you.