Linear Motion

Mass and Weight

Mass is the amount of matter (muscle, bone, fat and fluid) that makes up a body, measured in kilograms – it is a scalar quantity, since only size matters and it does not change with location (e.g. a rugby prop has far greater mass than a gymnast).

• Weight, by contrast, is a vector quantity – the gravitational force pulling a body toward the centre of the Earth:

Because gravitational strength is constant across the Earth's surface, a heavier performer's greater mass produces a correspondingly greater weight. This means an object's mass stays fixed wherever it is, but its weight would change on a planet/moon with different gravity (e.g. an object's weight on the moon is roughly a sixth of its weight on Earth, despite having identical mass in both places).

Distance and Displacement

Both distance and displacement describe how far a body has travelled, but differ in whether direction is taken into account.

• Distance is a scalar quantity – simply the total length of the path covered between a start and finish point, regardless of the route taken (e.g. one full lap of a 200m track covers a distance of 200m)
• Displacement is a vector quantity – the straight-line distance and direction from start to finish. In a full lap of a track, displacement is zero because the performer finishes where they started, even though the distance covered was 200m
• The difference is clearest in curved paths: a javelin throw or basketball free throw both follow a curved flight path (a greater distance travelled) while their displacement is the straight line from release/shot point to landing/basket

Speed and Velocity

Speed and velocity both measure how fast a body is moving, but again differ by whether direction is specified.

• Speed is a scalar quantity:

• Velocity is a vector quantity:

Velocity gives a more complete picture of motion because it also states the direction a performer or object is moving in.

Distance-Time Graphs

A distance-time graph plots the total distance a performer has covered against time, and the shape of the line reveals how their motion has changed.

• A flat horizontal section shows the performer is stationary, since no further distance is being covered as time passes
• A straight diagonal line shows the performer moving at a constant speed – the steeper the line's gradient, the greater that constant speed
• A curve that gets progressively steeper shows the performer accelerating, covering more distance in each successive time period (e.g. building up speed from a standing start); a curve that flattens out shows deceleration, as less distance is covered in each period near the end of a run

Velocity-Time Graphs

A velocity/speed-time graph plots velocity against time, and its gradient (the change in velocity divided by the change in time) reveals the performer's acceleration at any point.

• A flat horizontal line shows constant velocity, since the gradient – and therefore acceleration – is zero
• A line with a constant positive gradient shows constant (uniform) acceleration; a curve that gets progressively steeper shows increasing acceleration, as velocity is rising by a greater amount in each successive time period
• A downward-sloping section shows the performer is decelerating; if the line crosses below the time axis, this shows the body has reversed direction, since velocity is a vector and a negative value means motion is now happening the opposite way

Acceleration

Acceleration is the rate of change of velocity, measured in m/s² – it is a vector quantity. A rise in velocity is a positive acceleration, while a fall in velocity is a negative acceleration (deceleration).

This is often applied to split-time data, such as comparing a sprinter's velocity across consecutive 10m sections of a race, to see where in the race they were accelerating most and where their acceleration had levelled off.

Momentum

Momentum is the quantity of motion a moving body possesses:

Because it is calculated using velocity, momentum is itself a vector quantity.

• Since momentum depends on both mass and velocity, an increase in either factor increases a performer's overall momentum – a heavier player moving at the same speed as a lighter one will generate more momentum, and is therefore harder to stop or change direction (e.g. a prop forward vs a winger running at the same pace)
• Momentum is conserved when no external force acts on a body or object in flight – its momentum stays the same unless something (e.g. gravity, air resistance, or contact with another body) changes its velocity

Internal and External Forces

A force is required to change a body's state of motion, and forces acting during linear motion are grouped as either internal or external.

• An internal force is produced by the body's own skeletal muscles contracting – e.g. the quadriceps concentrically contracting to extend the knee when jumping
• An external force originates from outside the body, such as friction, air resistance, or gravity. Internal and external forces work together: internal muscular force allows a runner to generate the force needed to move, while external forces such as friction and air resistance act to resist that movement

Vertical Forces: Weight and Reaction

• Weight acts as a vertical force pulling a performer down toward the ground, equal to mass multiplied by the acceleration due to gravity
• Reaction force occurs whenever two bodies are in contact, and follows Newton's third law: for every action force there is an equal and opposite reaction force. When a footballer's boot strikes a ball, an action force is generated forward and down into the ball, while the ball exerts an equal and opposite reaction force back into the foot; when a foot contacts the ground while running, the ground produces an equal and opposite reaction force back into the foot, helping propel the runner forward

Horizontal Forces: Friction and Air Resistance

• Friction occurs whenever two surfaces in contact tend to slip or slide against one another, and always acts in the opposite direction to that potential/actual slipping motion – e.g. for a sprinter, the foot tends to slip backward on push-off, so the friction arrow acting on the foot points forward
• Friction is affected by: the surface characteristics of the two bodies in contact (rougher surfaces such as spiked running shoes increase friction and grip); the temperature of the two surfaces (e.g. sweeping the ice ahead of a curling stone slightly warms its surface, reducing friction so the stone travels further); and the mass of the object sliding, since a larger mass increases friction
• Air resistance is a form of drag that opposes a body's motion as it travels through air, and increases with: the velocity of the moving body (faster movement meets greater resistance); the cross-sectional area presented to the air (e.g. an upright cyclist meets more air resistance than one crouched low over the handlebars); and the shape/surface of the body, with smooth, streamlined shapes (e.g. a swimmer's shaved body and streamlined cap) reducing resistance compared with a rougher profile

Free Body Diagrams and Net Force

A free body diagram represents the forces acting on a performer at a single instant using arrows, where the arrow's length shows the size of the force, its starting point shows where it's applied, and its direction shows the direction the force acts in.

• The net (resultant) force is what remains once all forces acting on a body have been combined. If opposing forces are equal in size, the net force is zero and the body's state of motion does not change (a balanced state); if one force is larger than an opposing force, an unbalanced net force results and the body's motion changes accordingly – e.g. in a jump, if the reaction force exceeds bodyweight, the performer accelerates upward, and if propulsive friction exceeds resistance, a performer accelerates forward
• In events combining vertical and horizontal force, such as jumping, the ratio between the two components of the resultant force shapes the outcome – e.g. a high jumper's technique emphasises a large vertical force component to maximise height, whereas a long jumper emphasises a larger horizontal force component relative to vertical to maximise distance covered

Impulse and Force-Time Graphs

Impulse is the amount of time a force is applied for:

Since a change in momentum requires a force to be applied over some period of time, increasing impulse increases the resulting change in momentum, in line with Newton's second law.

• Impulse can be used deliberately to increase momentum by extending the time a force acts for or by increasing the force applied – e.g. a basketball player extending their arms and legs through a jump to generate a larger vertical impulse and jump higher, or a hammer thrower using several full turns to apply force over a longer time and build up greater release speed
• Impulse can equally be used to decrease momentum safely, by extending the time over which a force is absorbed – e.g. a gymnast bending the hips, knees and ankles on landing from the parallel bars to spread the impact over more time and reduce injury risk, rather than landing stiffly
• A force-time graph shows how force applied to the ground changes across a movement, with the area under the curve representing impulse. In sprinting, a large positive impulse phase occurs as the foot drives into the ground and the reaction force accelerates the athlete forward; a smaller negative impulse occurs as the foot lands and briefly decelerates the body, referred to as net impulse when the positive and negative portions are combined. Early in a sprint, positive impulse dominates (acceleration); mid-race, positive and negative impulses roughly balance (constant velocity); toward the end of a race as the athlete tires, negative impulse can begin to dominate (deceleration)