I need help with a limit problem

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keboehringer

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If a ball is thrown straight up into the air with an initial velocity of 40 ft/s, its height in feet after t second is given by y=40t−16t^2. Find the average velocity for the time period beginning when t=1 and lasting
  1. 0.1 seconds
  2. 0.01 seconds
  3. 0.001 seconds
  4. Finally based on the above results, guess what the instantaneous velocity of the ball is when t=1?
 
keboehringer said:
If a ball is thrown straight up into the air with an initial velocity of 40 ft/s, its height in feet after t second is given by y=40t−16t^2. Find the average velocity for the time period beginning when t=1 and lasting
  1. 0.1 seconds
  2. 0.01 seconds
  3. 0.001 seconds
  4. Finally based on the above results, guess what the instantaneous velocity of the ball is when t=1?
Click to expand...
Do you know the definitions of the average velocity and the instantaneous velocity?

Do you know the differences between the average velocity and the instantaneous velocity?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
The "average speed" between two times, \(\displaystyle t_1\) and \(\displaystyle t_2\), is the distance moved in that time interval divided by the the time, \(\displaystyle t_2- t_1\). The "period beginning at t= 1 second and lasting 0.01 sec" is from \(\displaystyle t_1= 1\) to \(\displaystyle t_2= 1.01\).

At t= 1 second the ball's height is \(\displaystyle 40(1)- 16(1)^2= 40- 16= 24\) feet.
At t= 1.01 seconds the ball's height is \(\displaystyle 40(1.01)- 16(1.01)^2= 40.4- 16(1.0201)=
23.6784\) ft. So how much higher or lower was the ball at 1.01 seconds that at 1 second?
 
Subhotosh Khan said:
Do you know the definitions of the average velocity and the instantaneous velocity?

Do you know the differences between the average velocity and the instantaneous velocity?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
Click to expand...
I've tried plugging each one into the equation, I've tried adding a 1 to each of the .1/.01/.001 but it always ends up wrong. I've tried dividing the answer I get from pluging it in and dividing it by the seconds I plugged in. Every answer I've came up with it says it's wrong.
 
keboehringer said:
I've tried plugging each one into the equation, I've tried adding a 1 to each of the .1/.01/.001 but it always ends up wrong. I've tried dividing the answer I get from pluging it in and dividing it by the seconds I plugged in. Every answer I've came up with it says it's wrong.
Click to expand...
Please share your work - if you want us to correct your mistake.

Just saying "it always ends up wrong" does not give us a clue. What makes you think "always ends up wrong"? What ends up being wrong?

If you want us to correct your mistake - we need to see "what" mistake did you make and "how" did you get there!
 
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