Question

The position of an object moving along a line is given by the function s(t)= -19t^2 + 171t. Find the average velocity of the object over the following intervals.

A.) [1,5] B.) [1,4] C.) [1,3] D.) [1,1+h] where h>0 is any real number

Answer 1

Answer:

a) 57

b) 76

c) 85

d) 133 - 19h

Step-by-step explanation:

Velocity is the derivative of position.

v(t) = s'(t) = $171-38t$

For the intervals [a, b], the average velocity is given by $\frac{v(a)+v(b)}{2}$.

a) [1, 5]

v = $\frac{v(1)+v(5)}{2} = \frac{133-19}{2}=57$

b) [1, 4]

v = $\frac{v(1)+v(4)}{2} = \frac{133+19}{2}=76$

c) [1, 3]

v = $\frac{v(1)+v(3)}{2} = \frac{133+57}{2}=85$

d) [1, 1+h]

v = $\frac{v(1)+v(1+h)}{2} = \frac{133+171-38(1+h)}{2}=\frac{266-38h}{2}=133-19h$