If the velocity of a moving body remains constant in both magnitude and direction with time, what is its acceleration?

Introduction / Context:
Acceleration describes how quickly the velocity of an object changes with time. If velocity changes in magnitude or direction, the object is said to be accelerating. Many problems in kinematics involve recognising when acceleration is zero and when it is not. This question asks what the acceleration is if the velocity remains constant in both magnitude and direction as time passes.

Given Data / Assumptions:

• The object has a velocity vector that does not change with time.
• Magnitude of velocity (speed) is constant.
• Direction of motion is also constant.
• We use the standard definition of acceleration as rate of change of velocity.

Concept / Approach:
Acceleration is defined as the time rate of change of velocity. If velocity is constant, then its value at any two instants is the same. The change in velocity over any time interval is zero, so the acceleration, which is change in velocity divided by time, must be zero. Non zero acceleration would imply that either the speed or the direction of motion changes. Since the question states that both are constant, acceleration must be zero.

Step-by-Step Solution:
Step 1: Write the definition of average acceleration: a = (v2 minus v1) / (t2 minus t1). Step 2: For constant velocity, v2 equals v1 for all time intervals, so the numerator v2 minus v1 is zero. Step 3: This gives a = 0 / (t2 minus t1) = 0, so average acceleration is zero over any time interval. Step 4: Instantaneous acceleration is the limit of average acceleration as the time interval becomes very small, which remains zero if velocity does not change. Step 5: Therefore, if velocity remains constant in both magnitude and direction, acceleration is zero.

Verification / Alternative check:
Consider a car moving in a straight line at 60 km per hour without speeding up, slowing down, or turning. Speedometer reading stays fixed, and there is no sideways or forward jerk felt by passengers. This real world example represents zero acceleration. In contrast, a car going around a circular track at constant speed experiences centripetal acceleration because direction changes, even though speed is constant. That situation does not match the condition given in this question, which specifies constant direction as well.

Why Other Options Are Wrong:
Constant but non zero: This would imply velocity is changing steadily with time, which contradicts the condition of constant velocity. Increasing with time: This suggests a growing acceleration and therefore a changing velocity, again contradicting the problem statement. Infinite: Infinite acceleration is not physically realistic in this context and would correspond to an instantaneous change in velocity, not constant motion.

Common Pitfalls:
Some learners think that any moving object must have some acceleration, confusing motion with change of motion. It is crucial to remember that acceleration is related to change in velocity, not just to velocity itself. If there is no change in speed or direction, there is no acceleration. Also, be careful to distinguish between constant speed with changing direction (which has centripetal acceleration) and constant velocity in a straight line, which has zero acceleration.

Final Answer:
If velocity is constant in both magnitude and direction, the acceleration of the body is 0.