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)=240x−16x^2​, 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)=240x−16x^2​, 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

​f(x)=240x−16x²

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

f'(x)' = v = 240 - 32x x = 7.5 seconds

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

When x=0, v = 240 ft/sec

When x=2

v = 240 - 32(2) = 64 feet/sec

​(C) The​ time(s) when v=0

0 = 240x−16x²

16x^{2 =} 240x 16x= 240

x = 0, 15 sec