Break into x and y: Ax=Acosθ, Ay=Asinθ.

Add the magnitudes directly: A = Ax + Ay.

Multiply the angle by the magnitude: Ax = θA, Ay = θA.

Use only the y-component: Ay = Asinθ.

Walking northeast can be split into north and east parts.

The number of apples in a basket.

The temperature of a room.

The color of a car.

Distance = total ground covered (scalar). Displacement = straight-line change from start to end (vector).

Distance = straight-line change from start to end (vector). Displacement = total ground covered (scalar).

Distance and displacement are both always equal for any motion.

Distance = shortest path between two points. Displacement = total path covered.

Speed = rate of distance change (no direction). Velocity = rate of displacement change (includes direction).

Speed = rate of displacement change (includes direction). Velocity = rate of distance change (no direction).

Speed and velocity both mean the same thing in physics.

Speed = rate of energy change. Velocity = rate of mass change.

Walking around a block (distance ≠ displacement).

Reading a book (distance = displacement).

Standing still (distance = displacement = 0).

Jumping up and down in place (distance ≠ displacement).

Motion along a straight line (with or without acceleration).

Motion in a circular path.

Motion in three-dimensional space.

Motion of fluids.

v = v0 + at; $$x = x0 + v0t + \frac{1}{2} at^2$$

v = v0 - at; $$1/2 at^2$$ x = x0 - v0t + $$1/2 at^2$$

$$v = v0 + 2at$$ ; $$x = x0 + v0t + at^2$$

v = v0 + at; $$1/2 at^2$$ x = x0 + v0t - $$1/2 at^2$$

A toy car speeding up in a straight track.

A book resting on a table.

A clock showing the same time.

A plant growing in a pot.

Velocity.

Acceleration.

Distance.

Time.

Acceleration.

Distance.

Velocity.

Time.

Displacement.

Speed.

Force.

Acceleration.

Fitness tracker speed chart.

Recipe ingredient list.

Book chapter summary.

Painting color palette.

Motion under gravity’s constant acceleration (g ≈ 9.8 m/s²).

Motion with constant speed in a straight line.

Motion only in the presence of air resistance.

Motion caused by an applied force other than gravity.

Same as 1-D kinematics, with a=ga = ga=g.

Only the equations for constant velocity apply.

Only horizontal motion equations apply.

Equations with variable acceleration only apply.

Dropping an apple.

Rolling a ball on a table.

Pushing a car.

Boiling water.

Horizontal (constant velocity) & vertical (accelerated by gravity).

Horizontal (accelerated by gravity) & vertical (constant velocity).

Rotational & translational motion.

Linear & circular motion.

Vertical acceleration + constant horizontal velocity.

Constant vertical and horizontal velocities.

No acceleration in any direction.

Only horizontal acceleration is present.

Tossing a ball.

Boiling water.

Reading a book.

Listening to music.

The velocity of one object measured from another’s frame: vA/B = vA − vB.

The sum of the velocities of two objects: vA/B = vA + vB.

The speed of an object in a vacuum: vA/B = vA × vB.

The velocity of an object relative to the ground: vA/B = vA.

Walking on a moving walkway in an airport.

Standing still in a park.

Reading a book at home.

Sleeping in bed.

Motion in a circle at constant speed, direction changes continuously.

Motion in a straight line at constant speed.

Motion in a circle at varying speed.

Motion in a straight line with changing speed.

Centripetal force.

Centrifugal force.

Gravitational force.

Frictional force.

ac = $$v^2/r$$ or $$rv^2$$ .

ac = $$r/v^2$$ .

ac = $$v/r^2$$ .

ac = $$r^2/v$$ .

Riding a Ferris wheel.

Reading a book.

Eating breakfast.

Writing a letter.