Slope of the velocity-time graph gives of a moving body. (A) displacement (B) acceleration (C) initial velocity (D) final velocity

The velocity-time graph is a graphical representation of the motion of a moving object that shows the object's velocity with respect to time. The graph has time represented on the x-axis while the instantaneous velocity is represented on the y-axis.

The slope of the graph is the rate at which one variable is changing with respect to another. In the case of a velocity-time graph, the slope represents the rate at which the velocity is changing with respect to time. Mathematically, the slope of the graph can be represented as: Slope = \(\frac{change\:in\:velocity}{change\:in\:time}\)

Now, we need to determine which concept from kinematics (displacement, acceleration, initial velocity, or final velocity) is represented by the slope of the velocity-time graph. Let's examine each option: (A) The slope of the graph cannot represent displacement, as displacement is the change in position, not the rate of change of velocity with respect to time. (B) Acceleration is defined as the rate at which velocity changes with respect to time. Therefore, the slope of the velocity-time graph can be represented as acceleration. Mathematically, acceleration is defined as: Acceleration = \(\frac{change\:in\:velocity}{change\:in\:time}\) (C) Initial velocity is the velocity of the body at the start of the time interval or when time is zero. It is not related to the slope of the graph, which represents the rate of change of velocity with respect to time. (D) Final velocity is the velocity of the body at the end of the time interval or when the motion stops. It also does not represent the slope of the graph, which indicates the rate of change of velocity with respect to time. Based on the above analysis, we can determine that:

The slope of the velocity-time graph represents (B) acceleration.