You will be able to
- Distinguish scalar quantities (distance, speed, mass, temperature) from vector quantities (displacement, velocity, acceleration) and state which applies in a gi
- Calculate total distance and displacement from a multi-segment motion along a number line.
- Compute average speed and average velocity over a time interval and explain why they can differ.
- Apply the constant-speed and constant-acceleration kinematic equations to one-dimensional motion problems.
- Convert units (meters per second to miles per hour) before substituting values into a kinematics formula, checking that units cancel.
Good to know first
- Basic arithmetic with positive and negative numbers
- Understanding of the x-axis as a number line with east/west or positive/negative directions
- Ability to solve a simple linear equation for one variable
Syllabus
7 lessons
- 1
Scalar vs. vector quantities Free
You will learn the difference between a scalar (magnitude only) and a vector (magnitude plus direction). You will sort common physics quantities into the two groups and see how distance and displacement differ.
1 formula3 exercises3 questions - 2
Distance vs. displacement on a number line Beyond Pass
Distance counts every meter you walk, so it is always positive and only adds up. Displacement only cares where you started and where you finished, so it can be positive, negative, or zero depending on direction.
1 formula2 exercises4 questions - 3
Speed vs. velocity and average values Beyond Pass
You will learn why distance and displacement differ, and why average speed (a scalar from total distance) and average velocity (a vector from displacement) can have different values. You will work through a particle that moves east then west to compute both.
3 exercises3 questions - 4
Instantaneous velocity and the delta notation Beyond Pass
This lesson explains how instantaneous velocity differs from average velocity and from instantaneous speed. It also teaches the delta notation (Δ) used to write changes in position, such as Δx = x_f − x_0.
2 exercises4 questions - 5
Constant speed and constant acceleration formulas Beyond Pass
This lesson shows the main kinematics formulas for constant speed (d = vt) and constant acceleration (the average-velocity form and the four standard equations). It explains when each one applies and how to tell distance from displacement.
4 formulas3 exercises3 questions - 6
Unit conversion and the bus problem: d = vt Beyond Pass
You learn how to use d = vt for constant speed, and why the units must match before you plug numbers in. You then convert 40 m/s into miles per hour by chaining conversion factors so the unwanted units cancel.
2 exercises4 questions - 7
Average velocity from displacement: the bus going west Beyond Pass
You learn to compute average velocity as displacement divided by time, using final and initial positions on a number line. You also learn that the sign of the answer tells you the direction of motion.
2 formulas3 exercises3 questions
Free preview · Lesson 1 in full
Scalar vs. vector quantities
You will learn the difference between a scalar (magnitude only) and a vector (magnitude plus direction). You will sort common physics quantities into the two groups and see how distance and displacement differ.
Draw and write next to the video.
The idea
Kinematics is the study of how objects move, described without talking about the forces that cause the motion. We start in one dimension, mostly along the x-axis. Before we can describe motion, we need a basic sorting tool: is a quantity a scalar or a vector?
A scalar quantity has magnitude only: a number with a unit, such as how much or how big. A vector quantity has both magnitude and direction. Mass is a scalar: a book has 2 kg of mass, and asking which way the mass points makes no sense. Distance is also a scalar: a person who walked 15 m has a distance of 15 m, but we have not said where they went.
Displacement is a vector. You can think of it as distance with direction. If a person walks 15 m east, we now know both how far and where, so we are describing displacement. Strictly, displacement is the change in position: along the x-axis it is the final position minus the initial position, written as .
Speed is a scalar: how fast an object is moving, such as 20 m/s. Velocity is a vector: speed with direction, such as 30 m/s north. Acceleration is also a vector, because it tells how fast the velocity is changing and it has a direction, such as 2 m/s² east. Temperature is a scalar: 80 °F has no direction, so you cannot say it points north.
Direction is only labelled on a line. On the x-axis, east is positive and west is negative. North and south lie along the y-axis. Distance and displacement can differ. Walk 30 m east, then turn and walk 4 m west. The total distance is 30 + 4 = 34 m, which is always positive. The displacement is +30 m + (−4 m) = +26 m, which points east. The two answers are different because distance adds up every step, while displacement only compares where you finished with where you started.
Key points
- A scalar has magnitude only; a vector has magnitude and direction. 0:33
- Mass and temperature are scalars, because direction does not apply to them. 0:54
- Displacement is distance with direction, and it is a vector. 1:50
- Speed is a scalar; velocity (speed with direction) is a vector. 2:45
- Acceleration is a vector because it has a direction. 3:20
- Distance adds every step (34 m) and is never negative; displacement is final minus initial position (+26 m east). 4:07
Formulas
Displacement equals the final position minus the initial position.
- displacement (a vector, with sign showing direction)
- final position along the x-axis
- initial position along the x-axis
Worked example
A person walks 30 m east, then turns around and walks 4 m west. Find the total distance and the displacement.
- East is positive, so the first walk is +30 m. West is negative, so the second walk is −4 m.
- Distance adds every part of the path without signs: 30 m + 4 m = 34 m.
- Displacement is the net change in position: +30 m + (−4 m) = +26 m.
- Since the sign is positive, the displacement points east.
Watch out
Practice
A runner goes 50 m north, then 20 m south. Find the total distance (in m) travelled by the runner.
Hint
Distance ignores direction, so just add the two lengths.
Solution
- Distance adds every part of the path without signs.
- Distance = 50 m + 20 m = 70 m.
70 m
Using the same runner (50 m north, then 20 m south), find the displacement in metres. Take north as positive.
Hint
Give north a plus sign and south a minus sign, then add.
Solution
- North is positive, so the first leg is +50 m and the second leg is −20 m.
- Displacement = final position − initial position = +50 m + (−20 m) = +30 m.
- The positive sign means the displacement is 30 m north.
30 m north
In your own words, explain why speed is a scalar but velocity is a vector, and give one example of each.
Solution
- Speed tells only how fast something moves, so it has magnitude only. Velocity is speed plus a direction, so it is a vector.
- Example: a car moving at 20 m/s is a speed; a car moving at 20 m/s east is a velocity.
Speed is magnitude only (e.g. 20 m/s); velocity adds direction (e.g. 20 m/s east).
On your scratchpad
Draw a horizontal x-axis with 0 in the middle, + on the right (east) and − on the left (west). Mark a start at 0, walk 30 to the right, then 4 to the left, and draw both arrows. Label the total distance and the displacement.
Quiz
Which of these is a vector quantity?
- Mass
- Temperature
- Velocity
- Distance
Show the answer
C. Velocity · Velocity is speed with direction, so it has both magnitude and direction. Mass, temperature and distance have magnitude only (around 0:33 to 2:17 in the video).
2:45 watch the momentA person walks 30 m east and then 4 m west. What is the displacement?
- 34 m east
- 26 m east
- 26 m west
- 4 m west
Show the answer
B. 26 m east · Displacement is final position minus initial position: +30 + (−4) = +26 m, which points east. The distance of 34 m is different because it counts all steps.
4:50 watch the momentWhich statement is correct about temperature?
- It is a vector because it can be hot or cold.
- It is a scalar because direction does not apply to it.
- It is a vector because 80 °F is a size and a direction.
- It is a vector because it changes.
Show the answer
B. It is a scalar because direction does not apply to it. · Temperature has only a magnitude, such as 80 °F, and you cannot say it points north. So it is a scalar.
3:30 watch the moment
Lessons 2–7
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Made by Beyond from the video “Kinematics In One Dimension - Physics” by The Organic Chemistry Tutor. The video plays in YouTube's own player. Watch it on YouTube · All lessons