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).
a. For the following functions s(t), find the instantaneous velocity function v(t). (Recall that the velocity function v is the derivative of the position function s.)
s(t)= −16t²+100t

Verified step by step guidance

1. Step 1: Identify the position function s(t) given in the problem, which is s(t) = -16t^2 + 100t.
2. Step 2: Recall that the instantaneous velocity function v(t) is the derivative of the position function s(t) with respect to time t.
3. Step 3: Differentiate the position function s(t) = -16t^2 + 100t with respect to t. Use the power rule for differentiation, which states that the derivative of t^n is n*t^(n-1).
4. Step 4: Apply the power rule to each term in s(t). The derivative of -16t^2 is -32t, and the derivative of 100t is 100.
5. Step 5: Combine the derivatives to find the velocity function v(t). Therefore, v(t) = -32t + 100.