Sept. 10 – D-T graphs and V-T grarphs

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Problem: How far away is the volcano?  The speed of sound is 340 m/s.

Time between explosion and sound can be found from watching the video.

Given:

∆t = 25 s – 12 s = 13 s

v = 340 m/s

Required:

∆d = ?

Analysis:

Isolate for ∆d.

v = ∆d / ∆t   —> rearrange —> ∆d = v ∆t

Solve:

∆d = (340 m/s)(13 s)

     = 4400 m

Statement:

The volcano is 4.4 km away.

Position-Time Graph (D-T graph)

• distance on the y-axis,
• time on the x-axis

The slope of the D-T graph represents speed (we recognized this from yesterday's activity)

If the ball is not moving, the slope is 0.

Speeding up and slowing down, give curved graphs.

Speeding up

 Slowing down

If the graph is a straight line (constant slope) we call it UNIFORM MOTION.

 - v is constant.

 - v= ∆d / ∆t  only works for uniform motion

y - intercept is the starting point of the motion

negative slope means the object is moving in the negative direction (backwards.)

Uniform Motion backwards

 Speeding up backwards

Slowing down backwards

Example: Describe the motion in this graph.

   - I leave my house and run 60 m.

   - I stop for 5 s.

   - I run back home and ran too far by 40 m.

   - I turn around and go back to home.

What is my total distance travelled?

d = 60 m + 0 m + 100 m + 40 m

   = 200 m

What is my displacement?

∆d = df  – di  = 0 m [forward] - 0 m [forward] 

                      = 0 m [forward]

Distance is the actual path travelled.

Displacement is the final change in position.

Example: Calculate the speed in each section of the trip.

Solutions:

v1 = 83 m/s

v2 = 42 m/s

v3 = 15 m/s

Velocity Time Graph (V-T graphs)

From the above data, we can draw a velocity time graph:

Homework

You should now be able to do homework from day 0 and day 1.

• HW:  Pg. 13 #1-4, 6,7
• HW:  Pg. 25 #1-3, 5-7, 9-13