Linear motion, also known as rectilinear or curvilinear motion, occurs when a body or object moves in a straight or curved line where all parts move at the same speed, in the same direction, and over the same distance.
In sports, true linear motion is rare because human movement is usually generated by the angular rotation of our joints. However, a sprinter running a 100-meter time trial down a straight track or a toboggan sliding down a bobsleigh run are excellent examples of linear motion.
Understanding this concept requires breaking down the forces that cause it, as well as the linear kinetics and kinematics used to describe it. To understand how linear motion is created, one must look at forces and Newton’s Laws of Motion. A force is a push or pull that alters the state of motion of a body. When a force is applied directly through the centre of mass of an object, it is called a direct force, and it results in linear motion without causing the object to spin.
Newton's First Law, the Law of Inertia, states that a body will remain at rest or in a state of uniform linear motion unless acted upon by an external force. For a sprinter in the blocks, they will remain stationary until they exert a massive force against the blocks, overcoming their inertia to move forward in a straight line.
Newton’s Second Law, the Law of Acceleration, explains that the acceleration of an object is directly proportional to the size of the force applied and takes place in the direction in which the force is applied. Mathematically, this is expressed as Force equals mass multiplied by acceleration ($F = ma$). If a shotputter applies a larger direct force to the shot, it will accelerate faster along its linear trajectory.
Newton’s Third Law, the Law of Action and Reaction, states that for every action, there is an equal and opposite reaction. When a runner pushes backwards and downward into the track, the track pushes them forward and upward with an equal force, propelling them into linear motion.
To describe linear motion, sports scientists measure specific quantities that are classified as scalars or vectors. Scalars only describe magnitude (size), whereas vectors describe both magnitude and direction. Distance is a scalar measure of the total ground covered by an object during its motion.
In contrast, displacement is a vector quantity representing the shortest straight-line distance from the starting point to the finishing point. For example, a swimmer completing one 50-meter lap of a 25-meter pool has covered a distance of 50 meters, but their displacement is exactly zero because they ended up right back where they started.
Similarly, speed and velocity describe how fast an object is moving. Speed is a scalar quantity calculated by dividing distance by time. Velocity is a vector quantity calculated by dividing displacement by time, meaning it includes the direction of travel.
Finally, acceleration is a vector quantity that measures the rate of change of velocity over time. An athlete accelerates when they speed up, change direction, or slow down.
By measuring these factors, coaches can analyse a sprinter's phase-by-phase velocity or a cyclist's acceleration out of a corner to pinpoint exactly where performance can be optimised.
