Help finding instantaneous velocity graphically

[murrayk91]

A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the instantaneous velocity at the following instants.

(a) t = 1.00 s

(b) t = 3.00 s

(c) t = 4.50 s

(d) t = 7.50 s

I know that a) is 5 m/s and c) is 0 m/s, but I need help figuring out b) and d). I don't understand how to draw the tangent line to find the instantaneous velocity.

For 3.00 s the answers I've come up with are wrong. I though using the slope of two points on the line, (7-10)/(3-2) should give me the answer. Any help?

 

[SammyS]

A graph of position versus time for a certain particle moving along the x-axis is shown in the figure below. Find the instantaneous velocity at the following instants.

(a) t = 1.00 s

(b) t = 3.00 s

(c) t = 4.50 s

(d) t = 7.50 s

I know that a) is 5 m/s and c) is 0 m/s, but I need help figuring out b) and d). I don't understand how to draw the tangent line to find the instantaneous velocity.

For 3.00 s the answers I've come up with are wrong. I though using the slope of two points on the line, (7-10)/(3-2) should give me the answer. Any help?

Since each of those times corresponds to a position at which the graph is a straight-line segment, and not where two segments meet, the slope of the tangent line is equal to the slope of the line segment.

You have the right idea with (7-10)/(3-2), it's just that the position at t = 3 s, is a bit in excess of 7 m. Use the whole segment from t = 2s to t = 4 s.

 

[SHISHKABOB]

When the average velocity doesn't change over a certain period of time, the instantaneous velocity is going to be the same.

It's like trying to find the average grade of five students who all got a 95 on the test

 

[murrayk91]

Thanks so much! I didn't realize I should take the slope of the whole line. I worked them out and they're correct.

 

[SammyS]

Good!

If you use the slope you got and go back to find what x is at t=3s, I think you'll find that x = 7.5m. It's hard to read the graph that accurately.