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A particle moves so that its position in m. as a function of time in sec is r equals i plus 4Tsqj plus tk. write expressions for a. its velocity and b. its acceleration as functions of time?
a. The velocity of the particle is the derivative of its position function with respect to time. In this case, the velocity would be v = 4t^2j + k. b. The acceleration of the particle is the derivative of its velocity function with respect to time. So, the acceleration would be a = 8tj.
When a particle is in motion its velocity is always in the direction of motion?
This is true by definition. Motion is defined by difference in position occurring as a function of time, and "velocity" is is thethree-dimensional vector which quantifies that motion. To simplify the concept to a single dimension, if "x" is the position of a particle on a line at any instant of time, then the velocity of the particle is defined as dx/dt, that is, the change in position x divided by the change in time as the change in time approaches zero as a limit.
Vector method to find out the acceleration of a particle is -wwrwhere angular velocity is w?
To find the acceleration of a particle using the vector method, you can use the equation a = r x (w x v), where "a" is the acceleration, "r" is the position vector, "w" is the angular velocity vector, and "v" is the velocity vector. The cross product (x) represents the vector cross product. By taking the cross product of the angular velocity vector with the velocity vector and then multiplying the result by the position vector, you can find the acceleration of the particle.
How can one derive the kinematic equations?
The kinematic equations can be derived by integrating the acceleration function to find the velocity function, and then integrating the velocity function to find the position function. These equations describe the motion of an object in terms of its position, velocity, and acceleration over time.
What is the velocity of the moving object at time 5 second?
To determine the velocity of a moving object at a specific time, you would need the object's position function or acceleration function. If you have the position function, you can differentiate it to get the velocity function and then substitute t=5 seconds. If you have the acceleration function, integrate it with respect to time to get the velocity function and then substitute t=5 seconds.
A particle moves so that its position in m. as a function of time in sec is r equals i plus 4Tsqj plus tk. write expressions for a. its velocity and b. its acceleration as functions of time?
a. The velocity of the particle is the derivative of its position function with respect to time. In this case, the velocity would be v = 4t^2j + k. b. The acceleration of the particle is the derivative of its velocity function with respect to time. So, the acceleration would be a = 8tj.
When a particle is in motion its velocity is always in the direction of motion?
This is true by definition. Motion is defined by difference in position occurring as a function of time, and "velocity" is is thethree-dimensional vector which quantifies that motion. To simplify the concept to a single dimension, if "x" is the position of a particle on a line at any instant of time, then the velocity of the particle is defined as dx/dt, that is, the change in position x divided by the change in time as the change in time approaches zero as a limit.
Vector method to find out the acceleration of a particle is -wwrwhere angular velocity is w?
To find the acceleration of a particle using the vector method, you can use the equation a = r x (w x v), where "a" is the acceleration, "r" is the position vector, "w" is the angular velocity vector, and "v" is the velocity vector. The cross product (x) represents the vector cross product. By taking the cross product of the angular velocity vector with the velocity vector and then multiplying the result by the position vector, you can find the acceleration of the particle.
According to the heisenberg uncertainty principle if the position of a moving particle is known what other cannot be known?
According to the Heisenberg uncertainty principle if the position of a moving particle is known velocity is the other quantity that cannot be known. Heisenberg uncertainty principle states that the impossibility of knowing both velocity and position of a moving particle at the same time.
What is the derivative of the position function?
the velocity function v= at + v(initial)
How can one derive the kinematic equations?
The kinematic equations can be derived by integrating the acceleration function to find the velocity function, and then integrating the velocity function to find the position function. These equations describe the motion of an object in terms of its position, velocity, and acceleration over time.
What is the velocity of the moving object at time 5 second?
To determine the velocity of a moving object at a specific time, you would need the object's position function or acceleration function. If you have the position function, you can differentiate it to get the velocity function and then substitute t=5 seconds. If you have the acceleration function, integrate it with respect to time to get the velocity function and then substitute t=5 seconds.
What is the Lagrangian for a particle moving on a sphere?
The Lagrangian for a particle moving on a sphere is the kinetic energy minus the potential energy of the particle. It takes into account the particle's position and velocity on the sphere.
What is maximum at mean position for particle performing simple harmonic motion?
Velocity is maximum at mean position for particle performing simple harmonic motion. Another feature that is maximum at this position is kinetic energy.
Find the displacement of a particle?
The displacement of a particle is the change in its position from its initial point to its final point, taking into account direction. It can be calculated as the difference between the final position and the initial position vector of the particle.
According to Heisenberg uncertainty principle if the position of a moving particle is known what other quantity cannot be known?
According to the Heisenberg uncertainty principle if the position of a moving particle is known velocity is the other quantity that cannot be known. Heisenberg uncertainty principle states that the impossibility of knowing both velocity and position of a moving particle at the same time.
How can one determine the position of an object based on its velocity?
One can determine the position of an object based on its velocity by integrating the velocity function over time. This will give the displacement of the object from its initial position.
