A particle of mass m is subject to a force (F) .Find the time dependent position x(t) of the particle for the following two cases : (a) F(x)=kx, with k>0, the initial position is `x_(0)`, and the initial speed is zero. (b) `F(v)=-bv^(2)` and the initial position is zero,and the initial speed is `v_(0)`.

A particle of mass m is acted upon by a force F= t^2-kx . Initially , the particle is at rest at the origin. Then

A particle of mass m kept at the origin is subjected to a froce vecF=(pt-qx)hati where t is the time elapsed and x is the x co-ordinate of the position of the particle. Particle starts its motion at t=0 with zero initial velocity. If p and q are positive constants, then:

A particle of mass m is subjected to a force vecF=F_(0)[cos (t)hati+sin(1)hatj] . If initially (t=0) the particle was at rest, the kinetic energy of the particle as a function of time is given by:

A particle of mass 0.3 kg subject to a force F=-kx with k=15N//m . What will be its initial acceleration if it is released from a point 20cm away from the origin?

A particle of charge q and mass m is subjected to an electric field E=E_(0)(1-ax^(2)) in the x - direction, where a and E_(0) are constants. Initially the particle was at rest at x = 0. Other than the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is :

A particle of mass 'm' and initially at rest is acted by a force F=a t. Newtons best representation of force-displacement graph is:

A body of mass 8kg is moved by a force F = (3x)N , where x is the disatance covered Initial position is x =2m and final position is x =10m If initially the body is at rest find the final speed .

A particle of mass 0.3 kg is subjected to a force F = - kx , Where = 15 Nm^(-1) . What will be its initial acceleration when particle is released from a point 20 cm away from origin ?