in search of a function

Question

An object is traveling in a straight line so that its position (that is, distance from some fixed point) is given by this table:

 

time (seconds) 0 1 2 3

distance (meters) 0 10 25 60

 

i need to the average speed a some intervals [0, 1], [0,2] etc,  i can work out the intervals ,but i cant think of a function to plug in the intervals. 

Answer 1

Here is 1 way. Not sure what your teacher has been teaching and what class you are in.

assume 3rd degree polynomial 

(You do this because you have 4 points you need to meet) 

 

x = A+Bt+Ct^2+Dt^3

plug in values of t 

0 = A

10 = B+C+D (1)

25=2B+4C+8D (2)

60=3B+9C+27D (3)

 

Solve for coefficients using forwards elimination and backwards substitution 

 

5=2c+6d (2)-2*(1) (2*)

30=6c+24D (3)-3*(1) (3*)

 

15=6D (3*)-2*(2*)

D = 5/2 = 2.5

from this C = -5

frkm this B = 12.5

 

so x = 12.5t-5t^2+2.5t^3 satisfies your problem.

Please let me know if you have any questions. Hope helpful.

Answer 2

for the speed:

 

v=(x_f-x_i)/(t_f-t_i)

 

for the acceleration:

 

a=(v_f-v_i)/(t_f-t_i)

 

for the distance:

 

x=x₀+v₀*t+(1/2)at²

 

 

 

for the average speed:

 

v_avg=(v_f-v_i)/2

 

tips:

 

arrange the data in a table of t vs. x:

 

find the change in x for each increment of t to find the speed for that increment of time.  

 

if you have any further problems please let me know.