Question

A ball is dropped from a height of 600 feet. The function describing the height of the ball at t seconds after it dropped is g src="https://tex.z-dn.net/?f=f%28t%29%3D-16t%5E2%2B600" id="TexFormula1" title="f(t)=-16t^2+600" alt="f(t)=-16t^2+600" align="absmiddle" class="latex-formula">.
a) Find the average velocity of the object during the first 3 seconds.

b) Verify that at some time during the first 3 seconds the instantaneous velocity equals the average velocity. Find that time.

The average velocity: _ ft/sec
The instantaneous velocity equals to the average velocity at t = _ sec

Answer 1

The average velocity of the object after during the first three seconds is: 48m/s

The time at which the instantaneous velocity equals the average velocity within the first three seconds is 1.5 seconds.

What is instantaneous and average velocities?

Instantaneous velocity  is the speed of an object at a particular point in time.

Average velocity is the velocity of an object after covering a certain distance for a period of time

Analysis:

Given

initial height = 600 feet

Height with respect to time = f(t) = -16$t^{2}$ + 600

a) Height at t = 0 = 600 feet

    Height at t = 3 seconds = f(3) = -16$(3)^{2}$ + 600 = 456 feet

Distance travelled  = 600 - 456 = 144 feet

Average velocity = distance travelled/time taken  = 144/3 = 48 feet/seconds

b) instantaneous velocity at time t = $\frac{df(t)}{dt}$ = $\frac{d(-16t^{2} + 600) }{dt}$ = -32t

  when instantaneous velocity equal average velocity

     -32t = -48

      t = 1.5 seconds

In conclusion, the Average velocity after 3 seconds is 48 feet per seconds and the time taken for the average velocity to equal the instantaneous velocity is 1.5 seconds.

Learn more about instantaneous and Average velocity: brainly.com/question/13372043

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