SPI Physics · Formula sheet

Kinematics and Motion formulas

4 formulas, 2 reference tables and 11 common traps for SPI Physics Kinematics and Motion, grouped by subtopic.

Distance, Displacement and Speed

Distance and displacement

\text{displacement} \le \text{distance} \qquad \text{circumference of a circle} = 2\pi r

Average speed over two or more parts of a journey

Average speed

\text{average speed} = \frac{\text{total distance}}{\text{total time}} \qquad 1\ \text{km/h} = \frac{5}{18}\ \text{m/s}

Rest and motion depend on what you compare with

Body	At rest compared with	In motion compared with
A passenger sitting in a moving bus	The bus and the other passengers	The road and the trees outside
A tree by the road	The ground	A passenger in a passing bus
A pilot flying a plane	The plane	The ground

Answer 'rest or motion?' with both, once you name the two reference points.

Common traps

Picking only one of rest and motion

A body can be at rest and in motion at the same time, compared with two different things. When the options include 'both', that is the answer for a passenger in a moving vehicle.

Giving the arc length as the displacement

On a circular path the arc is the distance. The displacement is the straight chord from start to end: across the full width of the circle, it is the diameter, 2r.

Thinking a full round is far away

After one complete round the body is back where it began, so the displacement is zero, even though the distance is

2\pi r

Averaging the two speeds

When the times are different, the mean of the two speeds is wrong. Find the total distance and the total time first; only equal TIMES make the simple mean right.

Using minutes with km/h

15 minutes at 8 km/h is

8 \times \frac{1}{4} = 2

km, not 120 km. Turn minutes into hours (divide by 60) before multiplying.

Motion Graphs and Equations of Motion

Learn this subtopic in the notes

Slope and area of a velocity-time graph

Velocity-time graph

a = \text{slope} = \frac{v - u}{t} \qquad \text{distance} = \text{area under the graph}

The three equations of motion and a body thrown upwards

Equations of motion

v = u + at \qquad s = ut + \tfrac{1}{2}at^2 \qquad v^2 = u^2 + 2as \qquad u = \sqrt{2gh} \text{ to reach height } h

$u$ starting velocity
$v$ final velocity
$a$ acceleration
$s$ distance (displacement)
$t$ time

What the shape of each motion graph means

Graph	Line shape	What the motion is
Distance against time	Flat	At rest
Distance against time	Straight, sloping up	Constant speed
Distance against time	Curving upwards	Speeding up
Velocity against time	Flat (above zero)	Constant velocity, so constant speed
Velocity against time	Straight, sloping up	Constant acceleration, speed changing
Speed against time	Straight, sloping up	Speed rising steadily
Acceleration against time	Flat (above zero)	Constant acceleration, speed changing

Constant speed shows up as a sloping distance-time line or a flat speed or velocity-time line.

Common traps

Reading a flat acceleration line as constant speed

A flat line on an acceleration-time graph means the acceleration is steady, so the speed is changing all the time. Constant speed needs zero acceleration.

Reading a flat distance-time line as constant speed

A flat distance-time line means the body is at rest. Constant speed on that graph is a straight line that slopes.

Mixing up slope and area

The slope of a velocity-time graph is the acceleration; the area under it is the distance. Area is never the acceleration.

Comparing two bodies by their speed at one moment

Which of two cars is ahead depends on the distance each has covered, which is the area under each graph up to that time, not on which one is faster at that instant.

Forgetting the speed at the top is zero

A body thrown up stops for an instant at its highest point. Put v = 0 there; that is what turns

v^2 = u^2 - 2gh

into

u = \sqrt{2gh}

Using the equations when acceleration changes

The three equations need steady acceleration. On a curved velocity-time graph, use the area and slope instead.

Kinematics and Motion formulas

Distance, Displacement and Speed

Average speed over two or more parts of a journey

Rest and motion depend on what you compare with

Common traps

Motion Graphs and Equations of Motion

Slope and area of a velocity-time graph

The three equations of motion and a body thrown upwards

What the shape of each motion graph means

Common traps

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