To find the net displacement, we need to consider the vector sum of all individual displacements. Displacement is a vector quantity, meaning it has both magnitude and direction. We can break down the movements into components along the East-West axis and the North-South axis.
The question asks for the net displacement, and the options are given in terms of single directions. This implies that the question might be simplified or misinterpreted in the options provided. However, let's re-evaluate the options based on the common competitive exam context where sometimes a single component is sought or a specific interpretation is expected.
Let's re-read the question and options carefully. The options are given as simple directions and magnitudes. This suggests that the question might be flawed or is looking for a specific component if it were a trick question. However, if we strictly follow the definition of net displacement, it should be \(3\sqrt{2}\) meters North-East.
Let's re-examine the problem statement to see if there's any ambiguity or a common simplification. The question asks for "net displacement\
To determine the relationship between velocity and acceleration for an object moving in a circular path, we need to understand the definitions and directions of these two vector quantities in such a motion.
C) Velocity and acceleration are perpendicular to each other. This is because velocity is tangential to the circular path, and centripetal acceleration is directed towards the center, making them always at a 90-degree angle to each other.
This question asks about the direction of acceleration for an object undergoing circular motion. Understanding the definitions of velocity and acceleration in circular motion is key to answering this question.
Correct Option: D) Directed towards the center of the circle. This is the definition of centripetal acceleration, which is always present in circular motion and is responsible for continuously changing the direction of the velocity vector, keeping the object on its circular path.
An object moves in a circle of fixed radius at constant speed. If the same object moves around the same circle at a higher constant speed, its centripetal acceleration:
Becomes zero
Decreases
Increases
Remains the same
The problem asks how the centripetal acceleration of an object changes when its speed increases while moving in the same circle. We need to recall the formula for centripetal acceleration and analyze its dependence on speed and radius.
Correct Option: C) Increases
If a force of 10 N is applied to an object with a mass of 2 kg for 5 seconds, what is the change in momentum of the object?
The problem asks for the change in momentum of an object when a force is applied for a certain duration. This can be directly calculated using the impulse-momentum theorem, which states that the impulse applied to an object is equal to the change in its momentum. Impulse is defined as the product of force and the time duration for which the force acts.
The impulse (\(J\)) applied to an object is equal to the change in its momentum (\(\Delta p\)).
\[ J = \Delta p \]Impulse is also defined as the product of the force and the time interval over which the force acts.
\[ J = F \times \Delta t \]Since \(J = \Delta p\), the change in momentum is:
\[ \Delta p = 50 \, \text{N s} \]C) 50NS — The change in momentum is equal to the impulse applied, which is the product of force and time (\(10 \, \text{N} \times 5 \, \text{s} = 50 \, \text{N s}\)).
The impulse-momentum theorem is a fundamental principle in physics that relates the impulse applied to an object to the change in its momentum. We need to identify the equation that correctly represents this relationship.
where \(F\) is the net force, \(p\) is the momentum, and \(t\) is time.
The left side of the equation, \( \int_{t_1}^{t_2} F \, dt \), is defined as the impulse (\(J\)). The right side is the change in momentum (\( \Delta p = p_2 - p_1 \)).
If the force \(F\) is constant over the time interval \( \Delta t \), then the impulse can be written as \( F \Delta t \). In this case, the theorem becomes:
\[ F \Delta t = \Delta p \]The options provided use \(F\) to represent the impulse itself, or a relationship between force and change in momentum. Option C, \(F = \Delta p\), is a simplified representation where \(F\) is understood as the impulse (which is \(F \Delta t\) for a constant force or the integral of force over time) or it implies that the impulse itself is represented by \(F\), which then equals the change in momentum.
C) \(F = \Delta p\). This equation represents the impulse-momentum theorem where \(F\) is often used to denote the impulse (which is the product of force and time interval, or the integral of force over time) and \( \Delta p \) is the change in momentum. More precisely, the impulse \(J = F \Delta t\) (for constant force) or \(J = \int F \, dt\) is equal to \( \Delta p \). In the context of multiple-choice questions, \(F = \Delta p\) is often used as a shorthand for the impulse-momentum theorem, implying that the impulse (represented by \(F\)) is equal to the change in momentum.