Question

The height above ground (feet) of a ball thrown straight upward is given by h(t)=3.5+8t-16t^2, where t is in seconds.

a) What is the average velocity of the ball during the first half second?

b) What is the ball's velocity at t=1/2?

c) What is the ball's acceleration at t=1/2?

Answer 1

Let's first take when it initially is in "rest", with that I mean t=0
So replacing:
\[h:h(t)=3.5+8t-16t ^{2} \]
si the image when t=0 is:
\[h:h(0)= 3.5+8(0)-16(0)^{2}=3.5\]

Answer 2

ok

Answer 3

average velocity is the slope of the line draw from time =0 to time = 1/2

Answer 4

for example your function looks something like this

Answer 5

Now you want to know in what's the image of h when t=1/2, can you do that?