The position of a falling object is given by the function

Question

s(t)=-16t^2+80t+10

(a) find the instantaneous velocity of the object at t=3/2.

(b) at what time t is the instantaneous velocity of the object zero?

Find the instantaneous velocity of the object at

t

=

3/

Find the instantaneous velocity of the object at

t

=

3/2

Find the instantaneous velocity of the object at

t

=

3/2

Find

Answer 1

Question: The position of a falling object is given by the function s(t) = -16t²+80t+10

(a) find the instantaneous velocity of the object at t=3/2.

(b) at what time t is the instantaneous velocity of the object zero?

Answer: We're given a position function. Recall that the velocity function is found by taking the derivative of the position function.

a. Apply differentiation across all three terms of s(t). We find that s'(t) = -32t + 80. Plug in (3/2) wherever you see t. s'(3/2) = -32(3/2) + 80 = 32.

b. The instantaneous velocity of the object is zero when s'(t) = 0. Make this substitution and solve for t:

( 0 ) = -32t + 80 --> -80 = -32t --> t = 2.5.