Kinematics

Displacement Plots

Finding Displacement Using V vs t Graphs

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Do Now warm-up prompt

Displacement Plots — finding displacement from V vs t graphs

Fill In The Blanks Notes

Warm-Up

This picture is of a single car moving across a room. The picture shows its position at equal time intervals. Describe its velocity.

Car moving across a room at equal time intervals

Video Instruction

showmethephysics.com

V. Finding Displacement Using V vs t Graphs

Velocity vs time plot, area under the curve highlighted

Since V = Δd/t

then Δd = Vt

= Area under the plot

= displacement (distance)

Ex

What is the displacement this object covered from t = 0 to t = 6 seconds?

↓

d = Area of the triangle

= ½bh

= ½(6 sec)(70 m/sec)

= 210 m

Ex 1

Object's displacement from t = 1 sec to t = 3 sec?

Velocity vs time plot, rectangle region
↓
Velocity vs time plot, rectangle region shaded

d = Area
= base × height

= (2 sec)(10 m/sec)

= 20 m

Ex 2

Object's displacement from t = 6 sec to t = 8 sec?

↓
Velocity vs time plot, trapezoid region shaded

d = area of trapezoid

= ½(h1 + h2) × base

= ½(25 m/s + 10 m/s)(2 sec)

= 35 m

Ranking Task

Smallest displacement?

Flash   showmethephysics.com

Ranking Task Answer — Largest B, Smallest D

AP Question

Ex 3

a) Find displacement after 4 seconds
b) At what time does the object return to its starting point?

Velocity vs time plot, positive and negative regions
↓

After 4 seconds

½(3 sec)(−10 m/s) + ½(1 sec)(10 m/s)

−15 m + 5 m

= −10 m

Answer: 5 seconds when d = 0

Ex 4

When did car A catch up to car B?

Velocity vs time plot for car A and car B
↓

Car A caught up to car B when their d are equal

At 60 sec:

Car B: d = 60 m/s(30 sec) = 180 m

Car A: d = ½(60 m/s)(60 sec) = 180 m

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. On a velocity vs. time graph, what does the area under the line represent?

2. An object moves at a constant 10 m/s from t = 1 s to t = 3 s. What is its displacement?

3. An object speeds up uniformly from 0 to 30 m/s in 4 s. What is its displacement?

4. An object's velocity changes uniformly from 10 m/s to 30 m/s over 2 s. What is its displacement?

5. On a V vs. t graph, the area above the time axis is 5 m and the area below is 15 m. What is the net displacement?

Free Fall →

Bonus

Amusing Surface Tension Experiment