Understanding Motion: Distance and Displacement

Motion

• Everyday life involves objects at rest and in motion.
• Atoms, molecules, planets, stars, and galaxies are in constant motion.
• Motion is perceived when an object's position changes with time.
• Indirect evidence, like air movement observed through dust or leaves, can imply motion.
• An object's state of motion (moving or stationary) is relative to the observer.
• Most motions are complex, involving straight lines, circular paths, rotation, or vibration, often in combination.

Describing Motion

• A reference point, or origin, is needed to describe an object's location.
• For instance, a school is 2 km north of the railway station. The railway station acts as the origin.

Motion Along a Straight Line

• The simplest form of motion occurs along a straight line.
• Distance is the total path length covered by an object, regardless of direction.
• Displacement is the shortest distance from the initial to the final position of an object.
• To describe distance is to specify only the numerical value and not the direction of motion.
• Magnitude is the numerical value of a physical quantity.
• Displacement includes both magnitude and direction.
• The magnitude of displacement can equal distance when there is only motion from start to end.
• However, magnitude of displacement can be zero even when the object has travelled some distance because it refers to the distance between the initial starting point and the final ending point.

Uniform and Non-Uniform Motion

• An object in uniform motion covers equal distances in equal time intervals.
• Non-uniform motion involves an object covering unequal distances in equal time intervals.

Measuring the Rate of Motion

• The rate of motion is measured by the distance an object travels in a unit of time, known as speed.
• The standard unit for speed is meters per second (m/s).
• The speed of an object does not have to be constant.
• Average Speed is the total distance travelled, divided by the total time taken.
• Average Speed = Total Distance / Total Time
• Velocity is the speed of an object moving in a definite direction.
• Velocity can be uniform or variable, and altered by changing speed, direction or both.
• When velocity changes at a uniform rate, average velocity is the arithmetic mean of initial and final velocities.
• Average velocity = (initial velocity + final velocity) / 2

Rate of Change of Velocity

• Acceleration measures the change in velocity of an object per unit time.
• Acceleration = change in velocity / time taken
• a = (v-u) / t, where a is acceleration, v is final velocity, u is initial velocity, and t is time.
• Acceleration is positive if it matches the direction of velocity and negative otherwise.
• The SI unit for acceleration is m/s².
• An object in uniform acceleration travels in a straight line and its velocity increases or decreases by equal amounts in equal time intervals.
• If velocity changes at a non-uniform rate, the object experiences non-uniform acceleration.

Graphical Representation of Motion

• Graphs effectively present basic motion information.
• Line graphs can depict the relationship between physical quantities like distance, velocity, and time.

Distance-Time Graphs

• Distance-time graphs illustrate the change in an object's position over time.
• Time is plotted on the x-axis, and distance on the y-axis.
• These graphs can represent uniform speed, non-uniform speed, or an object at rest.
• In uniform speed, the distance travelled is directly proportional to the time taken, represented by a straight line.
• The speed of an object can be determined using the slope of a distance-time graph.
• The equation for determining the speed of an object is v = (s₂- s₁) / (t₂– t₁) where v is speed.
• Distance-time graphs for accelerated motion are usually non-linear.

Velocity-Time Graphs

• These graphs depict the variation in velocity with time for an object moving in a straight line.
• Time is represented on the x-axis, and velocity on the y-axis.
• An object moving at a uniform velocity is represented by a straight horizontal line (parallel to the x-axis).
• The area enclosed by a velocity-time graph and the time axis equals the magnitude of the displacement.
• For uniformly accelerated motion, the velocity-time graph is a straight line.
• The distance travelled can be calculated from the area under a velocity-time graph: area = AB * BC + 1/2 (AD * DE).

Equations of Motion

• For objects moving along a straight line with uniform acceleration, a set of equations relates velocity, acceleration, time, and distance.
• v = u + at (velocity-time relation)
• s = ut + (1/2)at² (position-time relation)
• 2as = v² – u² (relation between position and velocity)

Uniform Circular Motion

• Acceleration occurs when the velocity of an object changes.
• This change can be in magnitude, direction, or both.
• An object that doesn't change in its magnitude of velocity but only its direction of motion also counts as acceleration.
• Motion of an object moving along a circular path is called uniform circular motion.
• The speed (v) of an object moving in this way is given by: v = 2πr/t, where r represents the radius and t represents the amount of time required.