A particle is moving along a straight line whose...

A particle is moving along a straight line whose velocitydisplacement graph is as shown in Fig. $6.2 .$ What is the acceleration when the displacement is $3 \mathrm{~m}$ ? a. $4 \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$ b. $3 \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$ c. $\sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$ d. $4 / \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$ Fig. $6.2$

A particle is moving along a straight line whose velocitydisplacement graph is as shown in Fig. $6.2 .$ What is the acceleration when the displacement is $3 \mathrm{~m}$ ?
a. $4 \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$
b. $3 \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$
c. $\sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$
d. $4 / \sqrt{3} \mathrm{~m} / \mathrm{s}^{2}$
Fig. $6.2$

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Key Concepts

Kinematics

Kinematics is the branch of mechanics that describes the motion of objects without considering the causes of motion. In problems involving motion along a straight line, it is essential to understand the relationships between displacement, velocity, and acceleration, which are typically analyzed through graphs and equations.

Velocity-Displacement Graph

A velocity-displacement graph plots the velocity of an object against its displacement. This type of graph can be used to obtain important information about the motion, such as calculating acceleration at a specific displacement point by observing the change in velocity with respect to displacement.

Chain Rule in Kinematics

The chain rule in calculus is a technique used to differentiate composite functions. In kinematics, it is applied to relate the derivatives with respect to time and displacement. Specifically, the acceleration (the derivative of velocity with respect to time) can be expressed as the product of the velocity and the derivative of velocity with respect to displacement (a = v (dv/dx)), which is crucial for analyzing motion when given a velocity-displacement relationship.

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