If an object moves along the​ y-axis (marked in​ feet) so that its position at time x​ (in seconds) is given by f(x)=182x−14x2, find the following.

Question

If an object moves along the​ y-axis (marked in​ feet) so that its position at time x​ (in seconds) is given by f(x)=182x−14x², find the following.

​(A) The instantaneous velocity function v=f′(x)

​(B) The velocity when x=0 and x=2 sec

​(C) The​ time(s) when v=0

Answer 1

(A) Velocity v'(x) = 182 - 28x;

(B) v(0) = 182 ft/s; v(2) = 182 - 28·2 = 126 ft/s

(C) v(x) = 0; 182 - 28x = 0; x = 182/28 = 6.5 s