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Displacement of a particle in x-y plane varies with time t is given by r=(t^2i +2j)m.Velocity of particle at t=1s is?
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Displacement of a particle in x-y plane varies with time t is given by...
Velocity of Particle at t=1s
Velocity is the rate of change of displacement with respect to time. In this case, the displacement of the particle in the x-y plane is given by the vector function r=(t^2i +2j)m.

Given:
r = t^2i + 2j m

Calculating Velocity:
To find the velocity of the particle at t=1s, we need to differentiate the displacement function with respect to time.
v = dr/dt
v = d(t^2i + 2j)/dt
v = 2ti

Substitute t=1s:
At t=1s, the velocity of the particle is:
v = 2(1)i
v = 2i m/s
Therefore, the velocity of the particle at t=1s is 2i m/s.
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Passage 2Newtons surprising success at developing the laws of motion, as well as the development and refinement of other physical laws, led to the idea of scientific determinism. The first expression of this principle was in the beginning of the nineteenth century by Laplace, a French scientist. Laplace argued that if one knew the position and velocity of all the particles in the universe at a given time, the laws of physics would be able to predict the future state ofthe universe.Scientific determinism held sway over a great many scientists until the early twentieth century, when the quantum mechanics revolution occurred. Quantum mechanics introduced the world to the idea of the uncertainty principle, which stated that it was impossible to accurately measure both the position and the velocity of a particle at one time. Because Laplaces omniscience could never occur, even in theory, the principle of scientific determinism was thrown into doubt. However, quantum mechanics does allow for a reduced form of scientific determinism. Even though physicists are unable to know precisely where a particle is and what its velocity is, they can determine certain probabilities about its position and velocity. These probabilities are called wave functions. By use of a formula known as the Schrodinger equation, a scientist with the wave function of a particle at a given time can calculate the particles future wave function. These calculations can give the particles position or velocity, but not both. Thus, the physicist is in possession of exactly half ofthe information needed to satisfy Laplaces view ofdeterminism. Unfortunately, under modern physics theories, that is far as any researcher can go in predicting the future.Q. The passage suggests that if scientific determinism were true

Passage 2Newtons surprising success at developing the laws of motion, as well as the development and refinement of other physical laws, led to the idea of scientific determinism. The first expression of this principle was in the beginning of the nineteenth century by Laplace, a French scientist. Laplace argued that if one knew the position and velocity of all the particles in the universe at a given time, the laws of physics would be able to predict the future state ofthe universe.Scientific determinism held sway over a great many scientists until the early twentieth century, when the quantum mechanics revolution occurred. Quantum mechanics introduced the world to the idea of the uncertainty principle, which stated that it was impossible to accurately measure both the position and the velocity of a particle at one time. Because Laplaces omniscience could never occur, even in theory, the principle of scientific determinism was thrown into doubt. However, quantum mechanics does allow for a reduced form of scientific determinism. Even though physicists are unable to know precisely where a particle is and what its velocity is, they can determine certain probabilities about its position and velocity. These probabilities are called wave functions. By use of a formula known as the Schrodinger equation, a scientist with the wave function of a particle at a given time can calculate the particles future wave function. These calculations can give the particles position or velocity, but not both. Thus, the physicist is in possession of exactly half ofthe information needed to satisfy Laplaces view ofdeterminism. Unfortunately, under modern physics theories, that is far as any researcher can go in predicting the future.Q. According to the passage, wave functions

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Displacement of a particle in x-y plane varies with time t is given by r=(t^2i +2j)m.Velocity of particle at t=1s is?
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