Find the average velocity for an object between t = 1 sec and t = 1.1 sec if f(t) = 5sin(t) + 5 represents its position in feet. (Round to the nearest thousandth.)
A) 2.702
B) 2.268
C) 2.487
D) -2.487

Question

Quizplus · Accepted Answer

To find the average velocity, we need to find the change in position (i.e., displacement) over the time interval and divide it by the duration of the interval. The displacement between t = 1 sec and t = 1.1 sec is given by:

f(1.1) - f(1) = [5sin(1.1) + 5] - [5sin(1) + 5]
= 5(sin(1.1) - sin(1))

Using a calculator, we can find that sin(1.1) = 0.891207 and sin(1) = 0.841471. Thus, the displacement is:

5(0.891207 - 0.841471) = 0.24868 feet

The duration of the interval is 0.1 seconds. Therefore, the average velocity is:

0.24868 feet / 0.1 seconds = 2.4868 feet/second

Rounding to the nearest thousandth gives:

2.487

Find the Average Velocity for an Object Between T =