Displacement () is a vector quantity that describes an object's change in position relative to a fixed reference point, often the origin. It is usually measured in metres (m) and can be positive, negative, or zero, indicating direction from the fixed point.
A positive displacement means the particle is in the positive direction from the fixed point, while a negative displacement means it is in the negative direction. Displacement is zero () when the object is precisely at the fixed reference point.
Distance () is a scalar quantity that represents the total path length an object has traveled, irrespective of direction. It is also measured in metres (m) but is always a positive value, as it only measures magnitude.
The key distinction is that displacement measures the net change in position, whereas distance measures the total ground covered. For example, a particle returning to its starting point will have zero displacement but a non-zero distance traveled.
Velocity () is a vector quantity that describes the rate of change of an object's displacement with respect to time. It is typically measured in metres per second ( or ) and indicates both the magnitude of motion and its direction.
A positive velocity signifies movement in the positive direction, while a negative velocity indicates movement in the negative direction. If the velocity is zero (), the particle is considered stationary or 'instantaneously at rest'.
Speed is a scalar quantity that represents the magnitude of an object's velocity, meaning it is the absolute value of velocity. It is also measured in metres per second ( or ) and is always a positive value.
Speed is essentially 'velocity ignoring the direction'; for instance, if , the speed is . This distinction is crucial because two objects can have the same speed but different velocities if they are moving in opposite directions.
Acceleration () is a vector quantity that describes the rate of change of an object's velocity with respect to time. It is measured in metres per second squared ( or ), which can be interpreted as metres per second per second.
Acceleration can be positive or negative, but its sign alone does not fully describe whether the particle is speeding up or slowing down. It indicates the direction in which the velocity is changing.
If the acceleration is zero (), it means the particle's velocity is constant, implying no change in either speed or direction. This does not necessarily mean the particle is at rest, only that its motion is uniform.
The direction of a particle's motion is solely determined by the sign of its velocity. A positive velocity means movement in the positive direction, and a negative velocity means movement in the negative direction.
A particle is accelerating (speeding up) when its velocity and acceleration have the same sign. This means both are positive (moving in positive direction and speeding up) or both are negative (moving in negative direction and speeding up).
Conversely, a particle is decelerating (slowing down) when its velocity and acceleration have different signs. For example, if velocity is positive and acceleration is negative, the particle is moving in the positive direction but slowing down.
Always read the question carefully to identify the fixed point for displacement and the chosen positive direction. If not specified, you may choose a positive direction but must remain consistent throughout the problem.
Pay close attention to the specific terminology used, as words like 'distance' and 'displacement' or 'speed' and 'velocity' have distinct technical meanings in kinematics. Misinterpreting these can lead to incorrect answers.
Remember that 'initial' or 'initially' always refers to the time . Similarly, 'instantaneously at rest' or 'stationary' implies that the velocity at that specific instant.
When analyzing motion, always consider the signs of both velocity and acceleration to determine if a particle is speeding up or slowing down. A common mistake is to assume negative acceleration always means slowing down, which is only true if velocity is positive.
