Question

The slope of the velocity-time graph for retarded motion is:
(a) Positive
(b) Negative
(c) Zero
(d) Can be positive, negative, or zero

Answer 1

Hint: The relationship between the velocity-time graph and the idea of the v-t graph must be understood in order to be able to answer this problem. The slope of the velocity-time graph, motion in a straight line, speed, and velocity all apply to this specific query. We are aware that acceleration is the rate of change of velocity per unit of time.

Complete answer:
Retardation is nothing but negative acceleration.
We know that \[{\rm{slope}} = \dfrac{{\Delta v}}{{\Delta t}}\]
For retardation we use $a = - \dfrac{{dv}}{{dt}}$

As from above we know that the rate of change of velocity per unit of time gives us acceleration same then the slope of the same graph will give acceleration.

The slope is defined as the ratio of vertical changes of two points to the horizontal change between similar points. As retardation means negative so the graph will also say negative.

Hence option (b) is correct.

Note: Similar to how the slope of the displacement time graph determines velocity, the area under the velocity-time graph displacement corresponds to the change in velocity, and the area under the acceleration time graph indicates the displacement.
In terms of mechanics(physics), acceleration is defined as the rate at which the velocity of an object changes with respect to time changes. They are vector quantities and accelerations. The direction of the net force applied to the item determines the object's acceleration.