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)?
(2t^{2} + 4t^{4}) W
(2t^{3} + 3 t^{4}) W
(2t^{3} + 3t^{5}) W
(2t + 3t^{3})W
If the velocity of a particle is v = At + Bt^{2}, where A and B are constants, then the distance travelled by it between 1 s and 2 s is,
3A + 7B
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
-2nβ^{2} x^{-2n-1}
-2nβ^{2 }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/s^{2}
0.18 m/s^{2}
0.2 m/s^{2}
0.2 m/s^{2}
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
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?
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
5 units
5 units