Question

Need Assistance if Anyone is Available.

Problem #09
In a time of t seconds, a particle moves a distance of s meters from its starting point, where s=4t^(2)+3.

(a) Find the average velocity between t=1 and t=1+h if:
(i) h=0.1
(ii) h=0.01
(iii) h=0.001

(b) Use your answers to part(a) to estimate the instantaneous velocity of the particle at time t=1.

Answer 1

use ur calculator

Answer 2

yeah i think i might be getting it actually
at t=1 s(t)=7

Answer 3

(i) h=0.1

t = `1` and t = 1+h = 1+0.1 = `1.1`

Answer 4

work t=1.1 also and find the average velocity

Answer 5

at t=1.1, s(t) = s(1.1) = ?

Answer 6

avg velocity for h=0.1 is 8.4m/s

Answer 7

very good ! thats the average velocity between 1 and 1.1 right ?

Answer 8

correct, let me do it for the other two real quick

Answer 9

okay

Answer 10

h=0.01 avg velocity is 8.04m/s
im just gonna guess that the avg velocity for h=0.001 is 8.004m/s which im sure it is.

so how do we find the instantaneous velocity now (for part b)?

Answer 11

whats instantaneous velocity ?

Answer 12

whats the meaning of instantaneous velocity ?

Answer 13

its the slope of the tangent or somethng right?

Answer 14

1 -> 1.1 : average velocity = `8.4`

1 -> 1.01 : average velocity = `8.04`

1 -> 1.001 : average velocity = `8.004`

Answer 15

slope of tangent line at t

Answer 16

it seems the nearer you getting to 1, the nearer the average velocity is getting to `8` right ?

Answer 17

yes exactly

Answer 18

can we assume the instantaneous velocity exaqctly at x=1 is 8 ?

Answer 19

yeah i would think so

Answer 20

Hi @nsellers23

Answer 21

your thinking is right ! the instantaneous velocity at x=1 is 8

Answer 22

well that wasnt all that hard at all, thanks gane! and hey pretty

Answer 23

Thank you @nsellers23