1. ## velocity

A toy rocket vertically in such a way that t seconds after lift-off, it is

h(t)= -1/2t^2 + 30t feet above ground.
a. How high is the rocket after 40 seconds?
b. What is the average velocity of the rocket over the first 40 seconds of flight (between
t

= 0 and
t = 40)?
c. What is the (instantaneous) velocity of the rocket at lift-off (t = 0)? What is the velocity

after 40 seconds?

2. Originally Posted by cclia
A toy rocket vertically in such a way that t seconds after lift-off, it is

[LEFT]h(t)= -1/2t^2 + 30t feet above ground.
a. How high is the rocket after 40 seconds?
do you understand how functions are defined? do you realize that h(t) gives the height at any time t? do you realize, for example, if i wanted to find the height after 2 seconds, this would simply be h(2)?

b. What is the average velocity of the rocket over the first 40 seconds of flight (between t= 0 and t = 40)?
there is a formula for this, it should not have been too hard to find in your text.

the average velocity between t = 0 and t = 40 is given by

$\frac {h(40) - h(0)}{40 - 0}$

c. What is the (instantaneous) velocity of the rocket at lift-off (t = 0)? What is the velocity after 40 seconds?
hint: the derivative gives us the formula for the instantaneous velocity