31–32. Velocity functions A projectile is fired vertically upward into the air, and its position (in feet) above the ground after t seconds is given by the function s(t).
b. Determine the instantaneous velocity of the projectile at t=1 and t = 2 seconds.
s(t)= −16t²+100t

Verified step by step guidance

1. Step 1: Understand that the instantaneous velocity of a projectile at a given time is the derivative of its position function s(t) with respect to time t. This derivative is denoted as v(t) = s'(t).
2. Step 2: Given the position function s(t) = -16t^2 + 100t, find the derivative s'(t) using the power rule. The power rule states that the derivative of t^n is n*t^(n-1).
3. Step 3: Apply the power rule to each term in s(t). The derivative of -16t^2 is -32t, and the derivative of 100t is 100. Therefore, s'(t) = -32t + 100.
4. Step 4: To find the instantaneous velocity at t = 1 second, substitute t = 1 into the derivative s'(t). Calculate v(1) = -32(1) + 100.
5. Step 5: To find the instantaneous velocity at t = 2 seconds, substitute t = 2 into the derivative s'(t). Calculate v(2) = -32(2) + 100.