Kinematics

The One Thing

Kinematics describes motion through position, displacement, velocity, acceleration, and time without considering the forces that cause the motion. Its central methods are the analysis of motion graphs, constant-acceleration equations, and the independent resolution of two-dimensional motion into perpendicular components.

Reactions, Processes and Experiments

In the equations of motion, $u$ is initial velocity, $v$ is final velocity, $a$ is constant acceleration, $t$ is time, and $s$ is displacement.

Key Terms

• Frame of Reference: A coordinate system and clock used to describe the position and motion of an object.
• Position: The location of an object relative to a chosen origin and coordinate system.
• Distance: The total length of the actual path travelled by an object; it is a scalar quantity.
• Displacement: The straight-line change in position from the initial point to the final point; it is a vector quantity.
• Speed: The rate of change of distance with time; average speed equals total distance divided by total time.
• Velocity: The rate of change of displacement with time; it has both magnitude and direction.
• Average Velocity: The total displacement divided by the total time interval.
• Instantaneous Velocity: The velocity of an object at a particular instant, equal to the slope of the position-time graph at that instant.
• Acceleration: The rate of change of velocity with time; acceleration may result from a change in speed, direction, or both.
• Uniform Motion: Motion in which an object covers equal displacements in equal intervals of time.
• Uniformly Accelerated Motion: Motion in which velocity changes by equal amounts in equal intervals of time.
• Scalar: A physical quantity described completely by magnitude, such as distance, speed, and time.
• Vector: A physical quantity having both magnitude and direction, such as displacement, velocity, and acceleration.
• Relative Velocity: The velocity of one object as measured from another object; for objects A and B, velocity of A relative to B is v_AB = v_A - v_B.
• Position-Time Graph: A graph showing how position changes with time; its slope gives velocity.
• Velocity-Time Graph: A graph showing how velocity changes with time; its slope gives acceleration and its area gives displacement.
• Acceleration-Time Graph: A graph showing how acceleration changes with time; its area gives the change in velocity.
• Projectile Motion: The motion of an object projected into the air under the influence of gravity, when air resistance is neglected.
• Uniform Circular Motion: Motion along a circular path with constant speed, although the velocity changes continuously because its direction changes.
• Components of a Vector: Perpendicular parts of a vector along selected axes; a vector can be resolved into horizontal and vertical components.

Easily Confused

• Distance and displacement: Distance is the total path length and is always non-negative; displacement is the straight-line change in position and may be positive, negative, or zero.
• Speed and velocity: Speed is a scalar rate of change of distance; velocity is a vector rate of change of displacement.
• Average speed and average velocity: Average speed uses total distance, whereas average velocity uses total displacement.
• Constant speed and zero acceleration: Constant speed does not necessarily mean zero acceleration, because a change in direction, as in uniform circular motion, changes velocity.
• Uniform motion and uniformly accelerated motion: Uniform motion has equal displacements in equal time intervals; uniformly accelerated motion has equal changes in velocity in equal time intervals.
• Position-time and velocity-time graphs: The slope of a position-time graph gives velocity, whereas the slope of a velocity-time graph gives acceleration.
• Velocity-time and acceleration-time graphs: The area under a velocity-time graph gives displacement, whereas the area under an acceleration-time graph gives the change in velocity.
• One-dimensional and two-dimensional motion: One-dimensional motion uses a single axis and signed quantities; two-dimensional motion requires perpendicular components and vector addition.
• Horizontal and vertical projectile motion: Horizontal acceleration is zero when air resistance is neglected, whereas vertical acceleration is $g$ downward.
• Distance and displacement on a return journey: An object can have zero displacement but non-zero distance if it returns to its starting point.
• Magnitude and direction of vectors: Displacement, velocity, and acceleration require both magnitude and direction; distance, speed, and time require magnitude only.

What Gets Asked

• Definitions and comparisons: Questions distinguish distance from displacement, speed from velocity, and scalar from vector quantities. Marks are lost by treating displacement or velocity as scalar quantities.
• Constant-acceleration calculations: Problems require selection of $v=u+at$, $s=ut+1/2a{t}^2$, $v^2=u^2+2as$, or $s=(u+v)t/2$. These equations apply only when acceleration is constant, and the symbols $u$, $v$, $a$, $t$, and $s$ must be assigned correctly.
• Graph interpretation: Questions ask for velocity or acceleration from a graph’s slope, and displacement or change in velocity from an area. A common error is interchanging slope and area, or using an unsigned area when direction matters.
• Vector resolution: Problems require $A_x=A\cos (theta)$, $A_y=A\sin (theta)$, and $A=$ square root of $(A_x^2+A_y^2)$. Marks are lost through incorrect component directions or failure to combine perpendicular components correctly.
• Projectile motion: Questions calculate horizontal and vertical velocities, time of flight, maximum height, or range. The main errors are applying gravity to the horizontal component, confusing the vertical and horizontal components, or using the same-level formula outside its stated conditions.
• Uniform circular motion: Questions test centripetal acceleration and the relation $v=\omega r$. The specific conceptual error is concluding that acceleration is zero because speed is constant, despite the continuous change in velocity direction.