Constant Acceleration / Motion Plots - Kinematics

Warm-Up

This pic shows the position of a basketball at even time intervals. Explain why you know the ball is accelerating.

Basketball positions at even time intervals

Motion Graphs [ HTML5 ] (d vs t)

Video Instruction

showmethephysics.com

B. Interpreting Motion Diagrams

Acceleration Review

a = ΔV/Δt = (V_f − V_i)/t

Uniform Acceleration? - constant change in velocity per unit time

Which data shows uniform acceleration? Why?

t (sec)	V (m/s)
0	5
1	7
2	9
3	11
4	13

t (sec)	V (m/s)
0	5
1	10
2	14
3	20
4	30

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Left Data Shows Constant Acceleration

a = 2 m/s²

Full Screen

Non-Constant or Constant Acceleration?

View the original GIF

Ex) Describe the acceleration

acceleration is constant +

Constant Non-Constant Acceleration?

Prove this is constant acceleration

Every 2 seconds the object gains exactly 15 m/s.

Motion Map — Velocity: 0 m/s / 15 m/s / 30 m/s / 45 m/s over 0 sec / 2 sec / 2 sec / 2 sec

↓

Find the acceleration: a = ΔV/Δt
= (+15 m/s)/2 sec

a = +7.5 m/s²

Motion Map — Acceleration: +7.5 m/s² every 2 seconds

Slope of a V vs. t Plot

Slope = Δy/Δx = ΔV/Δt = a

Ex) Describe motion using y axis and slope

Velocity vs time plot, constant velocity

Step 1: y axis: ? Step 2: Slope: ?

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Step 1: y axis: V constant

Step 2: Slope = ΔV/Δt
= a

a = 0

Ranking Task

Rank the acceleration from largest to smallest

January 2001 Regents

Ex 4

Velocity vs time plot, decreasing velocity

Step 1: y axis: ? Step 2: Slope: ?

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Velocity is Decreasing, Acceleration is constant, negative

Calculate the acceleration: a = (V_f − V_i)/t
= (15 m/s − 45 m/s)/(8 sec − 2 sec)

a = −5 m/s²

Video Instruction

showmethephysics.com

Ex 5

Describe the motions — Velocity (m/s)

Velocity vs time plot, increasing velocity

Step 1: y axis: ? Step 2: Slope: ?

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Step 1: y axis: V increasing

Step 2: Slope = ΔV/Δt
= a

a is increasing

Ex) Describe the Motions

Step 1: y axis: ? Step 2: Slope: ?

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Step 1: y axis: d increasing

Step 2: Slope = d/t
= V

Velocity is increasing smoothly

Acceleration is constant & Positive

Non-Uniform Acceleration

Ex) Describe Motions

Step 1: y axis: ? Step 2: Slope: ?

↓

Step 1: y axis: d increasing

Step 2: Slope = d/t
= v

Velocity is Decreasing smoothly (slope)

Acceleration is constant & negative

Describe Motions

d (cm)

Step 1: y axis: ? Step 2: Slope: ?

↓

Step 1: y axis: d constant

Step 2: Slope = d/t
= v

v = 0 (slope), a = 0

Analyzing Motion Plots

Analyzing Motion Plots - HTML5, Show Me The Physics

[Flash]

Try This at Home

Check Your Understanding

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

1. What is uniform acceleration?

2. An object's velocity is 4, 7, 10, and 13 m/s at t = 0, 1, 2, and 3 s. What describes its motion?

3. Starting from rest, an object gains exactly 15 m/s every 2 seconds. What is its acceleration?

4. A velocity vs. time graph is a flat horizontal line above the time axis. What is the acceleration?

5. An object's velocity drops from 45 m/s at 2 s to 15 m/s at 8 s. What is its acceleration?

NYSSLS Regents Practice · Kinematics · Analyzing Graphs

Cyclist Data Logger

A cyclist rode along a straight bike path with a speed sensor on her wheel. Graph 1 shows her velocity during one 12-second interval.

Graph 1: Velocity vs. Time

During which interval did the cyclist have the greatest magnitude of acceleration?

▶ Want a challenge? Open 6 more Regents-style questions (harder · mixed formats)

Challenge score: 0 / 6

Substitute values

C1. Substitute numerical values from Graph 1 into a mathematical representation that can be used to determine the cyclist’s displacement from 0 s to 4 s. Then calculate the displacement.

d = 12( s)( m/s) = m

Multiple choice

C2. Which statement describes the cyclist’s motion from 4 s to 10 s?

Support or Refute · Justify

C3. A student makes the following claim.

Claim: The cyclist traveled a greater distance while speeding up (0 s to 4 s) than while slowing down (10 s to 12 s).

Place a check mark in either the Support or Refute box. Justify your response using evidence from Graph 1.

Support Refute

Draw the vector · Determine the magnitude

C4. The cyclist rides to the right (east) the whole time. From 10 s to 12 s, choose the direction of her acceleration and determine its magnitude.

cyclist
●

a = m/s²

Multiple choice

C5. Which acceleration–time graph matches Graph 1?

Constructed response

C6. Describe how the cyclist’s average velocity for the 12-second interval can be determined from Graph 1, and explain why it is not equal to 8 m/s.

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