An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the object is at =+2 m, its velocity is $β4\hat{j}m/s$. The object's velocity (v) and acceleration (π) at π₯=β2 m will be
\(π£=β4\hat{i}\,m/s ,\,π=β8\hat{j} m/s^2\)
\(π£=β4\hat{i}\,m/s ,\,π=8\hat{j} m/s^2\)
\(π£=4\hat{i}\,m/s ,\,π=8\hat{j} m/s^2\)
\(π£=β4\hat{i}\,m/s ,\,π=8\hat{j} m/s^2\)
The Correct Option is C
Solution and Explanation
The object is moving in a circular path with constant speed. At \(x = +2 \, \text{m}\), the velocity is \(-4\hat{j} \, \text{m/s}\), indicating a downward motion.
At \(x = -2 \, \text{m}\), the velocity will be upward, i.e., \(+4\hat{j} \, \text{m/s}\).
The acceleration is centripetal and always directed toward the center of the circle. At \(x = -2 \, \text{m}\), the acceleration will point along the positive x-axis: \[ a = 8\hat{i} \, \text{m/s}^2 \]
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Concepts Used:
Kinematics
Kinematics is a branch of physics that deals with the study of motion, without considering the forces that cause the motion. It is concerned with the position, velocity, and acceleration of objects, as well as the time it takes for them to move from one point to another.
In kinematics, the motion of an object is represented using mathematical equations and graphs. The most common quantities used in kinematics are displacement, velocity, acceleration, and time.
Displacement refers to the change in position of an object, and it is represented by the symbol Ξx. Velocity is the rate at which an object's position changes over time, and it is represented by the symbol v. Acceleration is the rate at which an object's velocity changes over time, and it is represented by the symbol a.
Also Read: Kinematics Formula
By analyzing the relationships between these quantities, kinematics can be used to predict the motion of objects in different situations. For example, kinematics can be used to calculate the maximum height reached by a projectile, the distance traveled by a car during a given time, or the time it takes for a rollercoaster to complete a loop.
Kinematics is used in many areas of physics, including mechanics, astrophysics, and robotics. It is also used in engineering, where it is used to design and optimize the motion of machines and vehicles.