If a ball is thrown straight up into the air with an initial velocity of $80$ ft/s, its height in feet after $t$ seconds is given by $$y=80t−16t^2$$ Find the average velocity for the time period beginning when $t=1$ and lasting

(i) $0.5$ seconds

(ii) $0.1$ seconds

(iii) $0.01$ seconds

Finally, based on the above results, guess what the instantaneous velocity of the ball is when $t=1$.

  • $\begingroup$ Can you share your thoughts on the problem, and explain what you've tried? For example, do you know the definition of average velocity, or at least have a rough idea of what it means? $\endgroup$ – user61527 Oct 25 '13 at 6:53
  • $\begingroup$ Average velocity = distance/time $\endgroup$ – dnova Oct 25 '13 at 6:57
  • $\begingroup$ Yes. So can you find the distance and time for each part? $\endgroup$ – user61527 Oct 25 '13 at 6:58
  • $\begingroup$ Well that's where I'm stuck since what I've tried is plugging in the given values into my equation $\endgroup$ – dnova Oct 25 '13 at 6:59
  • $\begingroup$ Can you show what you've tried, then? $\endgroup$ – user61527 Oct 25 '13 at 6:59

The answer is $\frac{y(1+\delta)-y(1)}{\delta} = 16(3-\delta)$. Substitute the various values of $\delta$ above.

Since $\frac{dy(1)}{dt} = \lim_{\delta \downarrow 0} \frac{y(1+\delta)-y(1)}{\delta}$, you can estimate $\frac{dy(1)}{dt}$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.