Newton's backward Difference Formula Problem

[huzafa009]

The distance covered by an athlete for the 60 meter race is given in the following table. Determine the speed of the athlete at t=5 seconds, correct to 2 decimal places:

Time(seconds)	0	1	2	3	4	5	6
Distance(meter)	0	1.5	2.5	4.5	15.5	24.5	60

well i need to find average speed at t=5 ,sorry forgot to mention that formula used is Newton's backward Difference Formula



please solve it as soon as possible i would be a great help .

 

[Steven G]

The distance covered by an athlete for the 60 meter race is given in the following table. Determine the speed of the athlete at t=5 seconds, correct to 2 decimal places:

Time(seconds)	0	1	2	3	4	5	6
Distance(meter)	0	1.5	2.5	4.5	15.5	24.5	60

please solve it as soon as possible i would be a great help .

You are not given enough information to find the exact speed at t=5 second. You can find the average speed at t=5s. Where is your attempt? What formula can you use? How do you in every day life compute the average speed?

 

[huzafa009]

You are not given enough information to find the exact speed at t=5 second. You can find the average speed at t=5s. Where is your attempt? What formula can you use? How do you in every day life compute the average speed?

well i need to find average speed at t=5 by taking derivative at t=5 ,sorry forgot to mention that formula used is Newton's backward Difference Formula pic attached

 

[HallsofIvy]

What "help" do you want? You say you are to use "Newton's backward Difference Formula" which you show, involving $\displaystyle \nabla_1$, $\displaystyle \nabla_2$, etc. And you have an example, showing how to calculate each of those.
Here, the function values are 0, 1.5, 2.5, 4.5, 15.5, 24.5, 60. $\displaystyle \nabla_1$ for those are the "first differences", 1.5- 0= 1.5, 2.5- 1.5= 1.0, 4.5- 2.5= 2.0, 15.5- 4.5= 11.0, 24.5- 15.5= 9.0, and 60- 24.5= 35.5. $\displaystyle \nabla_2$ are the "second differences", 1.0- 1.5= -0.5, 2.0- 1.0= 1.0, 11.0- 2.0= 9.0, 9.0- 11.0= -2, and 35.5- 15.5= 20.0, etc.

 

[huzafa009]

What "help" do you want? You say you are to use "Newton's backward Difference Formula" which you show, involving $\displaystyle \nabla_1$, $\displaystyle nabla_2$, etc. And you have an example, showing how to calculate each of those.
Here, the function values are 0, 1.5, 2.5, 4.5, 15.5, 24.5, 60. $\displaystyle \nabla_1$ for those are the "first differences", 1.5- 0= 1.5, 2.5- 1.5= 1.0, 4.5- 2.5= 2.0, 15.5- 4.5= 11.0, 24.5- 15.5= 9.0, and 60- 24.5= 35.5. $\displaystyle \nabla_2$ are the "second differences", 1.0- 1.5= -0.5, 2.0- 1.0= 1.0, 11.0- 2.0= 9.0, 9.0- 11.0= -2, and 35.5- 15.5= 20.0, etc.

problem is my answer is not correct after solving it , so i want someone to solve it so i can check where iam wrong

 

[HallsofIvy]

Let's do it the other way around- you show us what you did and we can check and comment on it.