The position function of an object moving along a straight line is given by s=f(t). The average velocity of an object over the time interval [a,b] is the average rate of change of f over [a,b]; it’s velocity at t=a is the rate of change of f at a.A ball is thrown straight up with an initial velocity of 144ft/sec, so that it’s height (in feet) after t sec is given by s=f(t)= 144t-16t^2.(A)What is the average velocity of the ball over the following time intervals?[3,4]= ft/sec[3,3.5]= ft/sec[3,3.1]= ft/sec(B) what is the instantaneous velocity at time t=3? Ft/sec(C) what is the instantaneous velocity at time t=8? Ft/sec(D) when will the ball hit the ground?
Accepted Solution
A:
A) Position at time t = 3 s : s₁ = 144×3 - 16×3² = 288 ft Position at time t = 4 s : s₂ = 144×4 - 16×4² = 320 ft