The graph of position →time shown in the figure for a particle is not possible because ... (A) v

step 1 Hi student thanks a lot for posting the question welcome to the solution we have a position time

The graph of position →time shown in the figure for a...

The graph of position $\rightarrow$ time shown in the figure for a particle is not possible because ...
(A) velocity cannot have two values at one time
(B) Displacement cannot have two values at one time
(C) Acceleration cannot have two values at one time
(D) A, B and C are true

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Key Concepts

Kinematic Relationships

In kinematics, displacement, velocity, and acceleration are interconnected. Velocity is the derivative of displacement with respect to time, and acceleration is the derivative of velocity. If the position (displacement) were not uniquely defined at each time, the derived quantities (velocity and acceleration) could become ambiguous or undefined. Thus, ensuring that the position is a proper function is fundamental to accurately describing motion.

Position-Time Graph

A position-time graph in physics represents the displacement of a particle as a function of time. In such a graph, time is the independent variable and displacement must be uniquely defined for each value of time to satisfy the definition of a function. This means that at any specific moment, the particle can have only one position, and a graph that shows more than one position for a given time would violate this rule.

Function Properties in Mathematics

In mathematics, a function is defined as a relation wherein each input from the domain corresponds to exactly one output in the range. When applied to a position-time graph, time is the independent variable (input) and position is the dependent variable (output), which reinforces the principle that a particle cannot simultaneously occupy two different positions at the same time.

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