Question

If a body moves with uniform retardation, the velocity-time graph is a straight line
A. Inclined to the time axis with positive slope
B. Inclined to the time axis with a negative slope
C. Parallel to the time axis
D. Parallel to the velocity axis

Answer 1

Hint: Acceleration is defined as velocity per unit time, it is an increasing value. Use this definition to proceed. Use the velocity, acceleration and time relation, where retardation = - acceleration, use it to plot the graph.

Complete answer:
A body with uniform retardation means that it is decreasing , as retard means to reduce or decrease , at a constant rate with respect to time. Retardation is depicted by a negative slope and a negative value of acceleration, overall it’s just opposite of acceleration.
We know the relation $v = u + at$, where v is final velocity , u is initial velocity , a is acceleration , t is time taken.
So when retardation happens a becomes negative and the equation becomes $v = u - at$.
So the graph would be a straight line as it is in the form of y = c + mx.
The graph would look like

 

The red line shows the retardation of the body.
Also this line is inclined towards the time axis.

So, the correct answer is “Option B”.

Note:
Students must practise all the graphs associated with motion in a straight line which include displacement-time graph, speed-time graph, velocity- time graph etc., they help in solving the problem and are very important from exam point of view.