Kinetic energy of a charged particle is zero at time `t_(0)`. K at time 2 `t_(0)`. 2K at time 3 `t_(0)`. It remains constant (i.e.2K) upto 4 `t_(0)`. Choose the correct option.

The K.E. (K) of a charged particle is zero at time t, 2K at time 4t and 4k at time 5t and then it remains constant upto time 8t . Choose the correct statement/statements out of the following:

Kinetic energy of a particle moving in a straight line varies with time t as K = 4t^(2) . The force acting on the particle

Kinetic energy of a particle moving in a straight line varies with time t as K = 4t^(2) . The force acting on the particle

The kinetic energy of a particle varies with time according to the relation E_(k) = (8t + 6) K The force acting on the particle (k = constant)

A solid body A of mass m and specific heat capacity ‘s’ has temperature T_(1) = 400 K . It is placed, at time t = 0 , in atmosphere having temperature T_(0) = 300 K . It cools, following Newton’s law of cooling and its temperature was found to be T_(2) = 350 K at time t_(0) . At time t_(0) , the body A is connected to a large water bath maintained at atmospheric temperature T_(0) , using a conducting rod of length L, cross section A and thermal conductivity k. The cross sectional area A of the connecting rod is small compared to the overall surface area of body A. Find the temperature of A at time t = 2t_(0) .

A particle constrained to move along the x-axis in a potential V=k"x"^(2) is subjected to an external time dependent force vec(f)(t) here k is a constant, x the distance from the origin, and t the time. At some time T, when the particle has zero velocity at x = 0, the external force is removed. Choose the incorrect options – (1) Particle executes SHM (2) Particle moves along +x direction (3) Particle moves along – x direction (4) Particle remains at rest

Acceleration of a particle is given by a= 3t^(2)+2t +1 Where t is time . Find (i) its velocity at time t assuming velocity to be 10 m/s at t = 0. (ii) its position at time t assuming that the particle is at origin at t = 0. (iii) What is the average speed of the particle in the duration t = 0 to t = 1s? (iv) What is the average acceleration of the particle in the duration t = 0 to t = 1s?