Question

The path of an object can be modeled by the function f(t) = 5t^2 + 3 for all t > 0. Find each of the following:

The position of the object at t = 1 is:

The position of the object at t = 3 is:

The average speed of the object over the interval [1, 3] is:

Answer 1

To find the position of the object at different times, substitute the given values of t into the function f(t). The position of the object at t = 1 is 8 and at t = 3 is 48. To find the average speed over an interval, calculate the total distance traveled and divide it by the total time taken.

Step-by-step explanation:

To find the position of the object at a specific time, you need to substitute the given value of t into the function f(t).

For t = 1, the position of the object is f(1) = 5(1)^2 + 3 = 5 + 3 = 8.

For t = 3, the position of the object is f(3) = 5(3)^2 + 3 = 45 + 3 = 48.

To find the average speed of the object over the interval [1, 3], you need to calculate the total distance traveled and divide it by the total time taken.

The total distance traveled is f(3) - f(1) = 48 - 8 = 40, and the total time taken is 3 - 1 = 2. Therefore, the average speed is 40/2 = 20.