A body of mass 1kg is acted upon by a force `vec F=2sin3 pi hat i`+`3cos3 pi hat j `.Find its position at t=1sec if at t=0 it is at rest at origin.

A body of mass 1 kg is acted upon by a force vecF=2sin3pithati+3cos3pithatj find its position t=1 sec if at t=0 it is at rest at origin.

A body with mass 5 kg is acted upon by a force vec(F) = (- 3 hat (i) + 4 hat (j)) N . If its initial velocity at t =0 is vec(v) = 6 hat(i) - 12 hat (j) ms^(-1) , the time at which it will just have a velocity along the y-axis is :

An object of mass 3 kg is at rest. Now a force of vec F = 6 t^2 hat I + 4 t hat j is applied on the object, the velocity of object at t= 3 s is.

A body of mass 1 kg begins to move under the action of a time dependent force vec F = (2 t hat I + 3 t^(2) hat j) N , where hat i and hat j are unit vectors along x-and y-axes. What power will be developed by the force at the time t ?

A body is acted upon by a force vec(F) , given by vec(F)=-k[(cos omega t)hat(i)+(sin omega t) hat(i)] undergoes displacement, where the position vector vec(r) of the body is given by vec(r)=a[cos ( omega t+ alpha) hat(i)+ sin ( omega t+ alpha) hat(j)] . Find the work done by the force from time t=0 to time t=2pi//omega .

Given four forces : vec F_1 = 3 hat i - hat j + 9 hat k vec F_2 = 2 hat i - 2 hat j + 16 hat k vec F_3 = 9 hat i + hat j + 18 hat k vec F_4= hat i + 2 hat j - 18 hat k If all these forces act on a particle at rest at the origin of a coordinate system, then identify the plane in which the particle would begin to move ?

A rigid body consists of a 3kg mass located at vec r_1=(2hat i + 5 hat j)m and a 2kg mass located at vec r_2 = (4hat i +2 hat j)m . The position of centre of mass is

A force vecF=hat i+5 hat j+7 hat k acts on a particle and displaces it throught vec s=6 hat I +9 hat k . Calculate the work done if the force is in newton and displacement in metre. (ii) Find the work done by force vec F=2hat i-3 hat j+hatk when its point of application moves from the point A(1,2,-3) to the point B (2,0, -5).

A force vec F = (3t hat i + 5 hat j)N acts on a body due to which its position varies as vec S =(2t^2 hat i - 5 hat j) . Work done by this force in initial 2s is: