For a certain body, the velocity-time graph is shown in the...

For a certain body, the velocity-time graph is shown in the figure. The ratio of applied forces for intervals $A B$ and $B C$ is
(a) $+\frac{1}{2}$
(b) $-\frac{1}{2}$
(c) $+\frac{1}{3}$
(d) $-\frac{1}{3}$

Key Concepts

Force and Acceleration Relationship

Since the net force on a body is proportional to its acceleration, comparing the slopes of the velocity-time graph for different intervals (which correspond to different accelerations) directly provides insight into the ratio of the forces applied during those intervals. This concept is critical for solving problems that involve calculating force ratios from changes in the motion of the body.

Velocity-Time Graph Interpretation

A velocity-time graph is a graphical representation where velocity is plotted as a function of time. The slope of the tangent to the curve at any point on this graph indicates the acceleration of the body, while the area under the curve represents the displacement. This interpretation is essential for understanding how changes in velocity over specific time intervals relate to the forces acting on the body.

Acceleration and Slope

Acceleration is defined as the rate of change of velocity with respect to time and is represented by the slope of a velocity-time graph. A steeper slope implies a higher acceleration. Determining the slope for different time intervals on the graph allows for an analysis of how acceleration changes, which is directly related to the applied forces acting on the body.

Newton's Second Law

Newton's Second Law of Motion states that the net force acting on a body is equal to the mass of the body multiplied by its acceleration (F = ma). This law forms the basis for relating the change in motion (acceleration) observed on a velocity-time graph to the magnitude and direction of the applied forces.

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