Question

A position-time graph for a particle moving along the x axis is shown in the figure. The divisions along the horizontal axis represent 1.00 s and the divisions along the vertical axis represent 4.0 m.

Answer 1

(a) Find the average velocity in the time interval t = 3.00 s to t = 8.00 s.

Answer 2

(b) Determine the instantaneous velocity at t = 4.00 s (where the tangent line touches the curve) by measuring the slope of the tangent line shown in the graph.

Answer 3

(c) At what value of t is the velocity zero?

Answer 4

please help :) im in a calculus based physics course but in my calculus class we havent covered this yet :)

Answer 5

pic of problem

Answer 6

a. average velocity is distance at 8s minus distance at 3s, divided by (8s-32) = 5s.

b. slope of the tangent line is (0 - y) m /(4-0) s

c. velocity is zero where the curve is briefly horizontal.

Answer 7

can you explain how you find b in detail :)

Answer 8

slope m = (ending y - stating y) / (ending x - starting x)
or m = (y2 - y1)/(x2 - x1)

Answer 9

i can take a zoomed in pic if needed

Answer 10

i know horiztonal goes up by 1 s per line and vertical is 4 m per line

Answer 11

Thanks, what I want you to do is to find the initial y and final y values and do the same for the initial and final x values.

Answer 12

i know there wanting a negative answer

Answer 13

You will get a negative answer because the final y is smaller than the initial y,
while the final x is greater than the initial x.

Answer 14

this should help :))

Answer 15

now since tangent lines derivatives and limits are things I havent covered yet, what point should i look for excatly to find the intial and final values

Answer 16

They tell you and show you that the tangent line starts at the intersection with the y axis and is continued
to an intersection with the x axis, so these two points should be evident.

Answer 17

should i use the final point as the zero x value at the end of the line on point (7s,0)?

Answer 18

yes, and the initial point is the intersection with the y axis, (0,y)

Answer 19

i dont think i see the y value too well it appears as a decimal right near the point where the curve starts touching the slope

Answer 20

like i said this is all new content to me. were on 1.3 in calculus which is trig functions and inverses

Answer 21

i did find the average velocity and the velocity at 0 just cant see this instaneous velocity too well

Answer 22

They drew the tangent line for you. If they had not, and you wanted to calculate it, you would go the region of interest, 4.00 s, and calculate the change in y and the change in x in the immediate vicinity, for example, using the values of y here at x=3s and x=5s as approximations.