Kinematics connects three quantities through rates of change. A position-time graph shows where the object is; its slope gives velocity. A velocity-time graph shows how velocity changes; its slope gives acceleration and its area gives displacement. Always read the axis before choosing a graph feature.

Position gives location relative to an origin; displacement is change in position.

Velocity is rate of change of displacement and is the gradient of a position-time graph.

Acceleration is rate of change of velocity and is the gradient of a velocity-time graph.

Area under a velocity-time graph gives displacement for the chosen direction.

Interpret the graph features that connect position, velocity, and acceleration.

Graph

A position-time graph and a velocity-time graph are shown for the same one-dimensional motion.

1Identify the position-time graph feature that gives velocity.

2Identify the velocity-time graph feature that gives acceleration.

3Identify the velocity-time graph feature that gives displacement.

Which graph feature gives velocity, which gives acceleration, and which gives displacement from a velocity-time graph?

A student says that the gradient of a position-time graph gives acceleration. Correct the statement and give the graph feature that gives acceleration.

Confusing graph features because the axes were not checked.

A student says that the gradient of a position-time graph gives acceleration. Correct the statement and give the graph feature that gives acceleration.

Choose

Rate of change is the language behind kinematics definitions. Average values use a finite interval, while instantaneous values use the gradient at a point. The numerator must match the quantity being described: displacement for velocity and velocity for acceleration.

A rate of change compares how much a quantity changes with the time taken.

Average velocity is Δx/Δt; average acceleration is Δv/Δt.

Instantaneous values are found from the tangent gradient at one instant.

Units follow from the ratio: m s^-1 for velocity and m s^-2 for acceleration.

Use a graph to distinguish average and instantaneous rate of change.

Graph

A curved position-time graph has a secant line across a time interval and a tangent at one instant.

1Identify the interval quantity.

2Identify the point quantity.

3State the unit for velocity.

What does the secant gradient give, and what does the tangent gradient give?

A car changes velocity from 4.0 m s^-1 to 16.0 m s^-1 in 3.0 s. Calculate its average acceleration and state what would be needed for an instantaneous acceleration.

Using velocity/time instead of change in velocity over time.

A car changes velocity from 4.0 m s^-1 to 16.0 m s^-1 in 3.0 s. Calculate its average acceleration and state what would be needed for an instantaneous acceleration.

Choose

Displacement describes the straight-line change in position, not the path taken. In one dimension, choose a positive direction, read initial and final positions, and subtract initial from final. The sign carries the direction.

Position is measured relative to an origin.

Displacement is Δx = x_final - x_initial.

Displacement is a vector, so sign or direction matters.

A negative displacement means final position is in the negative direction from the initial position.

Label the displacement diagram on a position axis.

Label

Labels

5

An object moves from x = -3 m to x = +5 m. Calculate its displacement and explain why the path taken is not needed.

Using total path length instead of final minus initial position.

An object moves from x = -3 m to x = +5 m. Calculate its displacement and explain why the path taken is not needed.

Choose

Distance and displacement answer different questions. Distance asks how much ground was covered. Displacement asks how far and in what direction the final position is from the starting position.

Distance is total path length and is a scalar.

Displacement is straight-line change from start to finish and is a vector.

Distance is never negative; displacement can be positive, negative, or zero depending on direction.

A round trip can have non-zero distance and zero displacement.

Sort each statement as distance or displacement.

Sort

Unsorted

6

distance

0

displacement

0

A runner completes one 400 m lap of a track and finishes at the starting line. State the distance and displacement.

Giving displacement as 400 m because the path length was 400 m.

A runner completes one 400 m lap of a track and finishes at the starting line. State the distance and displacement.

Choose

Average quantities summarize a whole interval. Instantaneous quantities describe a single time. For velocity, direction matters; for speed, only magnitude matters. Graph questions often reveal which is needed by asking for an interval or a specific instant.

Average speed is total distance divided by total time.

Average velocity is total displacement divided by total time.

Instantaneous speed or velocity describes one moment.

On graphs, instantaneous velocity is the tangent gradient of a position-time graph.

Choose whether each situation asks for an average or instantaneous value.

Decision

Speed at exactly t = 4.0 s.

Total distance divided by total journey time.

Gradient of tangent to a position-time graph at one point.

Gradient of secant line between two times.

A cyclist travels 1200 m in 200 s, but the speedometer reads 8.0 m s^-1 at t = 50 s. Identify the average speed and the instantaneous speed.

Treating the speedometer reading as average speed for the whole trip.

A cyclist travels 1200 m in 200 s, but the speedometer reads 8.0 m s^-1 at t = 50 s. Identify the average speed and the instantaneous speed.

Choose

SUVAT is a selection process, not a memorized substitution. First check constant acceleration. Then write down s, u, v, a, and t with units and signs. The useful equation is the one that includes the unknown and does not require the one missing quantity.

SUVAT equations apply only when acceleration is constant and motion is one-dimensional.

The five quantities are s, u, v, a, and t.

Choose a positive direction and list known values with signs.

Pick the equation that contains the unknown and avoids the missing quantity.

Build the SUVAT selection method before substituting values.

Formula

Target formula v^2 = u^2 + 2as

s

displacement

m

u

initial velocity

m s^-1

v

final velocity

m s^-1

a

constant acceleration

m s^-2

t

time

s

1Check that acceleration is constant.SUVAT valid only for constant a

2List s, u, v, a, t and identify the missing variable.t is not needed

3Choose the equation without t.v^2 = u^2 + 2as

4Apply the chosen positive direction to all vector quantities.s, u, v, a may be positive or negative

Build the formula

A student uses SUVAT for a falling object with large air resistance. Explain why this may be invalid.

Forgetting that SUVAT requires constant acceleration.

A student uses SUVAT for a falling object with large air resistance. Explain why this may be invalid.

Choose

Uniform acceleration is about the gradient of the velocity-time graph. If the gradient is constant, acceleration is constant. If the gradient changes, acceleration is non-uniform and SUVAT cannot be used directly for the whole interval.

Uniform acceleration means acceleration is constant.

A straight line on a velocity-time graph shows uniform acceleration.

A curved velocity-time graph shows acceleration changing with time.

SUVAT equations are valid only for uniform acceleration.

Repair mistakes about uniform acceleration and SUVAT validity.

Spot Errors

A velocity-time graph is a curve with increasing gradient. Explain whether SUVAT can be used over the whole interval.

Seeing a smooth graph and assuming acceleration is constant.

A velocity-time graph is a curve with increasing gradient. Explain whether SUVAT can be used over the whole interval.

Choose

Projectile motion becomes manageable when split into perpendicular components. The horizontal component has no acceleration in the ideal model, while the vertical component follows constant acceleration under gravity. The two components share the same time.

A projectile moves under gravity alone after launch in the ideal model.

Horizontal velocity is constant when air resistance is negligible.

Vertical acceleration is g downward near Earth’s surface.

For launch speed u at angle θ, u_x = u cosθ and u_y = u sinθ.

At maximum height, vertical velocity is zero, but horizontal velocity is not zero.

Build the component model for an ideal projectile.

Formula

Target formula u_x = u cos theta; u_y = u sin theta; a_x = 0; a_y = -g

u

launch speed

m s^-1

theta

launch angle above horizontal

degrees or radians

u_x

horizontal component of initial velocity

m s^-1

u_y

vertical component of initial velocity

m s^-1

g

gravitational field strength near Earth

m s^-2

1Resolve the initial velocity horizontally.u_x = u cos theta

2Resolve the initial velocity vertically.u_y = u sin theta

3Set horizontal acceleration for the ideal model.a_x = 0

4Set vertical acceleration with upward positive.a_y = -g

Build the formula

A ball is launched at speed u at angle θ. State the horizontal and vertical initial velocity components and the accelerations for ideal projectile motion.

Setting horizontal acceleration equal to g or setting horizontal velocity to zero at maximum height.

A ball is launched at speed u at angle θ. State the horizontal and vertical initial velocity components and the accelerations for ideal projectile motion.

Choose

Fluid resistance breaks the simple projectile assumptions. Drag always acts opposite the instantaneous velocity, so it changes direction during the flight. The vertical acceleration is no longer simply g downward throughout the motion, and the horizontal component is no longer constant.

Air resistance opposes the projectile’s velocity.

With significant air resistance, the trajectory is not a perfect parabola.

Range and maximum height are usually reduced compared with the no-drag model.

Acceleration is not constant because drag changes with speed and direction.

Terminal speed occurs when drag balances weight during downward motion.

Repair incorrect statements about air resistance on projectiles.

Spot Errors

Describe two ways air resistance changes the motion of a projectile compared with the ideal no-drag model.

Saying only that “it slows down” without linking drag direction, acceleration, or trajectory shape.

Describe two ways air resistance changes the motion of a projectile compared with the ideal no-drag model.

Choose

A.1 is secure when the student reads the quantity before choosing a formula or graph feature. The common thread is rate of change: position changes into velocity, velocity changes into acceleration, and graphs show those links through slope and area.

Displacement is vector change in position; distance is scalar path length.

Velocity is rate of change of displacement; acceleration is rate of change of velocity.

Graph gradients and areas depend on axes: x-t gradient gives velocity, v-t gradient gives acceleration, v-t area gives displacement.

SUVAT equations apply only to one-dimensional motion with constant acceleration.

Ideal projectile motion has horizontal constant velocity and vertical acceleration g downward.

Air resistance makes acceleration non-uniform and the trajectory non-parabolic.

Match each A.1 retrieval cue to the correct response.

Match

Reasons

0/9

IB Physics HL A.1 Kinematics Notes

Read Motion with Three Quantities

Use Rate of Change

Turn Position Change into Displacement

Separate Path Length from Vector Change

Average or Instantaneous?

Choose the Right SUVAT Equation

Spot Uniform Acceleration

Split Projectile Motion into Components

Analyze Fluid resistance on projectiles

Retrieve the A.1 Kinematics Model