If `a = x^(2)` find velocity when x = is 2m given at x = 0 body is at rest ​

A particle of mass 10^-2kg is moving along the positive x axis under the influence of a force F(x)=-K//(2x^2) where K=10^-2Nm^2 . At time t=0 it is at x=1.0m and its velocity is v=0 . (a) Find its velocity when it reaches x=0.50m . (b) Find the time at which it reaches x=0.25m .

If a car accelerates with acceleration depend on displacement as a =6x^(2)+2x+5 . Find velocity of particles when it is at x=3m.Given that initially it starts from x=1 with velocity 2 m/s.

At t=0 , a body starts from origin with some initial velocity. The displacement x(m) of the body varies with time t(s) as x=-(2//3)t^2+16t+2 . Find the initial velocity of the body and also find how long does the body take to come to rest? What is the acceleration of the body when it comes to rest?

Acceleration of a particle is given by a =1//V Where V is the velocity . Find (i) Velocity of particle at time t, given that v = 10 m/s at t = 0. (ii) Velocity of particle when its position is x, given that speed is 3 m/s at x = 0.

(1 + x^(2)) (dy)/(dx) + 2xy = 4x ^(2) , given that y = 0 , when x =0

Given that x varies directly with the square of y. when x is 2,y is also 2. find y when x is 8. given that it is positive.

If velocity is given by following function V = x^2 . Then find out relation between x & t (assume x = 1 m at t = 0)

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 .

The equation of a travelling wave is y(x, t) = 0.02 sin ((x)/(0.05) + (t)/(0.01)) m Find (a) the wave velocity and (b) the particle velocity at x = 0.2 m and t = 0.3 s . Given cos theta = -0.85 , where theta = 34 rad

Acceleration of a particle is given by a = 2x (i) It’s velocity at position x. Given that v = 10 m/s when x = 0. (ii) Minimum speed that the particle can attain