Understanding Motion with Constant Velocity

Let's analyze the properties of an object moving with constant velocity to determine which statement is not correct. Constant velocity means that both the speed and the direction of motion remain unchanged over time. Velocity is a vector quantity, having both magnitude (speed) and direction. If velocity is constant, its magnitude (speed) is constant, and its direction is constant.

Analyzing Statements about Constant Velocity Motion

We will examine each given statement based on the definition of constant velocity:

• Statement 1: Its motion is along a straight line.

  For an object to have constant velocity, its direction must not change. Motion in a constant direction occurs along a straight path. Therefore, if velocity is constant, the motion must be along a straight line. This statement is correct.

• Statement 2: Its speed changes with time.

  Constant velocity implies that the magnitude of the velocity vector, which is speed, remains constant over time. If the speed were to change, the velocity would not be constant. This statement contradicts the definition of constant velocity.

• Statement 3: Its acceleration is zero.

  Acceleration is defined as the rate of change of velocity (\(\vec{a} = \frac{d\vec{v}}{dt}\)). If the velocity (\(\vec{v}\)) is constant, then its rate of change is zero. Therefore, an object moving with constant velocity has zero acceleration. This statement is correct.

• Statement 4: Its displacement increases linearly with time.

  For motion with constant velocity (\(\vec{v}\)), the displacement (\(\Delta \vec{r}\)) over a time interval (\(\Delta t\)) is given by the equation \(\Delta \vec{r} = \vec{v} \Delta t\). If \(\vec{v}\) is constant, the magnitude of the displacement (\(|\Delta \vec{r}|\)) is directly proportional to the time interval (\(\Delta t\)), provided \(\vec{v}\) is not zero. This direct proportionality means that the displacement increases linearly with time. This statement is correct.

Identifying the Incorrect Statement

Based on the analysis, the statement that is NOT correct for an object moving with constant velocity is "Its speed changes with time". Constant velocity means the speed is constant, not changing.

Revision Table: Key Concepts of Constant Velocity

Additional Information on Velocity and Acceleration

It is important to distinguish between speed and velocity, and between velocity and acceleration.

• Speed is a scalar quantity that describes how fast an object is moving. It is the magnitude of velocity.
• Velocity is a vector quantity that describes both how fast an object is moving (speed) and in what direction it is moving.
• Acceleration is a vector quantity that describes the rate at which velocity changes. Velocity can change either by a change in speed or a change in direction (or both). If velocity is constant, there is no change in speed or direction, hence acceleration is zero.

Even if an object moves at a constant speed, if its direction changes (like in uniform circular motion), its velocity is not constant, and it is accelerating (specifically, centripetal acceleration).

Conversely, if an object is accelerating, its velocity is changing. This change could be in speed, direction, or both. If acceleration is constant (but non-zero), velocity changes linearly with time, but the motion is along a straight line only if the acceleration is in the same or opposite direction as the initial velocity.