A body of mass 1 kg begins to move under the action of a time dependent force F =  N, where  are units vectors along X and Y axis. What power will be developed by the force at the time (t)?

• (2t² + 4t⁴) W

• (2t³ + 3 t⁴) W

• (2t³ + 3t⁵) W

• (2t + 3t³)W

If the velocity of a particle is v = At + Bt², where A and B are constants, then the distance travelled by it between 1 s and 2 s is,

• 3A + 7B

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A particle  moves so that its position vector is given by r = cos  where  is a constant. Which of the following is true?

• velocity and acceleration both are parallel to r

• velocity is perpendicular to r and acceleration is directed towards the origin

• velocity is perpendicular to r and acceleration is directed away from the origin

• velocity and acceleration both are perpendicular to r

A particle of unit mass undergoes one-dimensional motion such that its velocity according to
V(x) =  βx^-2n where β and n are constants and x is the position of the particle. The acceleration of the particle as a function of x is given by 

• -2nβ² x^-2n-1

• -2nβ² x^-4n-1

• -2β x^-2n+1
  

• -2β x^-2n+1
  

What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

A particle of mass 10 g moves along a circle of radius 6.4 cm with a constant tangential acceleration. What is the magnitude of this acceleration, if the kinetic energy of the particle becomes equal to 8 x 10^-4 J by the end of the second revolution after the beginning of the motion?

• 0.15 m/s²

• 0.18 m/s²

• 0.2 m/s²

• 0.2 m/s²

A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle  with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is,

• 3.5

• 5.9

• 16.3

• 16.3

108.

A balloon with mass m is descending down with an acceleration a (where a <g). How much mass should be removed from it so that it starts moving up with an acceleration a?

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The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

A particle has initial velocity (2i+3j) and acceleration (0.31i +0.2j). The magnitude of velocity after 10 s will be

•  units
•  units

• 5 units

• 5 units