Measurement toolkit; position, distance, and displacement

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The SI base units
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Metric prefixes: kilo-, centi-, milli-
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Convert a prefixed unit to the base unit
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Convert between km/h and m/s
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Count a measurement's significant figures
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Round a result to the right precision
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Position: a signed coordinate
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The frame of reference
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Moving or at rest? Name the frame first
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Distance traveled: the whole path
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Displacement: start to finish
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Calculate displacement: Δx = x − x₀
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Distance or displacement? They can disagree

Speed and velocity; scalars and vectors

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Speed or velocity? The direction test
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Average velocity: displacement divided by time
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A velocity's sign is its direction of motion
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Calculate average velocity with v = Δx / Δt
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One journey, two averages: speed and velocity
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Instantaneous velocity: the velocity right now
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Instantaneous or average? Ask when it belongs
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Scalars: complete with a size alone
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Vectors: a size plus a direction, drawn as an arrow
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Sort the motion quantities: scalar or vector
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Pick the quantity for the job: scalar or vector

Acceleration

Watch any car for one minute. It moves off from a light, settles to a cruise, swings through a corner, brakes for a crossing. Hardly any of that minute is spent at one steady velocity.

This topic is about changing velocity. You will learn the name physics gives it, the equation and the unit that measure it, and the sign rules that say whether a motion is speeding up or slowing down.

Nine lessons, and each teaches one skill. The first asks a simpler question than you might expect: what counts as a change in velocity at all?

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When a velocity changes
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Accelerating means any change in velocity
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Which acceleration is greater?
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The acceleration equation: a = Δv/Δt
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Read the unit m/s²
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Calculate an acceleration: find Δv first
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The sign of an acceleration
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Speeding up or slowing down: the sign rule
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Use the sign rule on real motions

Motion graphs 1: position-time

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Read a position-time graph
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The slope of a position-time graph is the velocity
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Calculate the velocity from a straight segment
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Describe the motion from the shape of the line
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Which way is it moving? The sign of the slope
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Construct a position-time graph from a journey
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Find the flaw in an offered graph

Motion graphs 2: velocity-time

The last few lessons turned a journey's positions into one picture. This set of lessons draws a new picture of the same kind of journey: the object's velocity, moment by moment. One line on one pair of axes is about to answer four different questions: how fast, which way, speeding up or slowing down, and where the object ends up. How can a single line carry all of that?

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Read a velocity from a velocity-time graph
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Read the direction of motion from the side of the axis
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Speeding up or slowing down: toward or away from the axis
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The slope of a velocity-time graph is the acceleration
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Calculate an acceleration from the slope
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The area under the line is the displacement
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Why the area gives the displacement
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Calculate a displacement from the area
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Find the moment of reversal: the axis crossing
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Construct a velocity-time graph from a description
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Find the flaw in an offered velocity-time graph

Motion graphs 3: acceleration-time, and linking the three

One motion can be told three ways: where the object is, how fast it moves, and how quickly its velocity changes. You can already read the first two graphs. This topic adds the third, and then makes all three tell one story on a shared clock.

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Read an acceleration-time graph
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The area under an acceleration-time graph: the change in velocity
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Calculate a velocity change from an acceleration-time graph
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Draw the velocity-time graph from an acceleration-time graph
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Draw the acceleration-time graph from a velocity-time graph
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Check an acceleration-time graph against its velocity-time graph
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Sketch the velocity-time graph from a position-time graph
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Sketch the position-time graph from a velocity-time graph
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One motion, three graphs: build the aligned stack

Kinematic equations

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The kinematic equations and when they apply
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The first kinematic equation: v = v₀ + at
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Calculate a final velocity with v = v₀ + at
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The second kinematic equation: Δx = v₀t + ½at²
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Calculate a displacement with Δx = v₀t + ½at²
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The no-time equation: v² = v₀² + 2aΔx
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Solve with the no-time equation
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The fourth kinematic equation: Δx = ½(v₀ + v)t
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Solve with the average-velocity equation
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Why the average-velocity equation works
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Choosing the right equation
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Rearranging v = v₀ + at
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Rearranging Δx = v₀t + ½at² for the acceleration
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Rearranging v² = v₀² + 2aΔx
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Trips with more than one stage
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The equation on the graph

Free fall

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Free fall: when gravity acts alone
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The free-fall acceleration g
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Same fall, any mass
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Signs in free fall: choose a direction and keep it
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A dropped object's velocity after a time
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How long a drop takes
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Thrown upward: the velocity, second by second
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At the very top
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Why the acceleration is not zero at the top
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How long to the top
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How high it rises
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The rise and the fall take equal times
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Same height, same speed
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The whole flight