The table shows the position of a cyclist. t (seconds):0,1,2,3,4,5. s (meters): 0,1.4,5.3,10.5,17.4,25.1. Find Average Velocity at points [1,3] [2,3] [3,5] [3,4]. Find instantaneous velocity when t=3

Answer 1

t f(t)

0 0

1 1.4

2 5.3

3 10.5

4 17.4

5 25.1

to find the average velocity: from xA to xB, the formula is [ f(xB) - f(xA)] / (xB - xA)

for example, the average velocity from t=3 to t=5 is [ f(5) - f(3) ] / (5-3) =

(25.1 - 10.5) / 2 =

14.6/2 =

7.3

The others are found the exact same way!!!

the answers are

For the instantaneous velocity, we need the position function.

quadratic regression gives:

C= -0.225

B =1.22178571

A= 0.776785714

where

y = At^2 + Bt +C = 0.776785714t^2 + 1.221785714t -0.225

the derivative is 1.5535714285t + 1.2217857142

at t=3, the instantaneous velocity is 5.8825928582, and this is an APPROXIMATION