Derivative for average velocity

[Dorian Gray]

Greetings Mathematicians,

I have come across a math problem that has been giving me some difficulties.


Problem: The displacement (in meters) of a particle moving in a straight line is given by s=t squared - 8t + 18 where t is measured in seconds.

A. Find the average velocity over each time interval
i. [3,4] ii [3.5,4] iii. [4,5] and iv [4,4.5]


B. Find instantaneous velocity when t=4


Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a) and the tangent line whose slope is the instantaneous velocity in part (b).



OK. I am having issues with part A. I do not know where to start. I know think I am supposed to use the [ f(a + h) - f(a) ] / [h]. However, I do not know how I am supposed to apply those time intervals to the equation.

Any help, comments, suggestions are all appreciated.

 

[Deleted member 4993]

Greetings Mathematicians,

I have come across a math problem that has been giving me some difficulties.


Problem: The displacement (in meters) of a particle moving in a straight line is given by s=t squared - 8t + 18 where t is measured in seconds.what about measurement unit of s?

A. Find the average velocity over each time interval
i. [3,4] ii [3.5,4] iii. [4,5] and iv [4,4.5]


B. Find instantaneous velocity when t=4


Draw the graph of s as a function of t and draw the secant lines whose slopes are the average velocities in part (a) and the tangent line whose slope is the instantaneous velocity in part (b).



OK. I am having issues with part A. I do not know where to start. I know think I am supposed to use the [ f(a + h) - f(a) ] / [h]. However, I do not know how I am supposed to apply those time intervals to the equation.

Any help, comments, suggestions are all appreciated.

Make a table:

t	s
3	3
3.5	2.25
4	2
4.5	2.25
5	3

for average velocity during t = 3 and t = 3.5, you have

s₃ = 3

s_3.5 = 2.25

v_avg = (2.25 - 3)/(3.5 -3) = - 1.5


Now is the problem bit clearer.....

 

[Dorian Gray]

thank you

Thank you very much Sobhotosh Khan. I greatly appreciate your help.