Question

For a uniformly retarded motion, the velocity time graph is:
A) Curve
B) a straight line parallel to time axis
C) a straight line perpendicular to time axis
D)a straight line inclined to time axis

Answer 1

Hint: For uniformly retarded motion the value of acceleration is always constant but negative , this negative non -zero acceleration is called retardation which shows velocity is decreasing continuously with time and velocity – time graph for this type of motion can never be parallel or perpendicular to time axis.

Complete answer:
When velocity of a body decreases with time uniformly then it is defined as uniformly retarded motion. Retardation can be represented mathematically by the negative value of acceleration which means velocity of the body is decreasing uniformly with a constant rate. Value of retardation is a non-zero constant.

This graph represents that velocity is decreasing with time uniformly so this graph represents uniformly retarded motion. In this graph a straight line is formed inclined to the time axis making some obtuse angle from x axis in anticlockwise direction.
Slope of Velocity – Time graph represents the acceleration of the body.
Slope of the line is represented by\[Tan\theta \].
Let us assume the acceleration of the body is represented by a.
\[\Rightarrow a=Tan\theta \]
Where \[\theta \]is the angle from x-axis to line of graph in anticlockwise direction.
When \[\theta \] is acute,\[\theta <{{90}^{0}}\] then\[Tan\theta \]is positive which represents uniform acceleration of the body.
When \[\theta \] is obtuse, \[\theta >{{90}^{0}}\]then \[Tan\theta \]is negative which represents uniform retardation of the body
When the line is parallel to the time axis which means \[\theta ={{0}^{0}}\]that means acceleration is zero which means either the body is moving with constant velocity or at rest.
When a line is perpendicular to the time axis then it means the velocity is increasing or decreasing with time and is constant which is not possible because time can never be constant and mathematical value of slope becomes not defined.
When velocity time graph is a curve then it shows accelerated or retarded motion but that motion of body is not uniform which means acceleration or retardation changes continuously with time.

Correct Option is D .

Note:
The time rate of change of velocity of an object is called acceleration of the object. Acceleration is a vector quantity. Its direction is the same as that of change in velocity (Not of the velocity). A body is said to have uniform acceleration if magnitude and direction of the acceleration remains constant during particle motion.