A small cart A starts moving on a horizontal surface, assumed to be x-y plane along a straight line parallel to x-axis (see figure) with a constant acceleration of `4 m//s^(2)`. Initially it is located on the positive y-axis at a distance 9 m from origin. At the instant the cart starts moving, a ball is rolled along the surface from the origin in a direction making an angle `45°` with the x-axis. The ball moves without friction at a constant velocity and hits the cart.
(a) Describe the path of the ball in a reference frame attached to the cart.
(b) Find the speed of the ball.

On a frictionless horizontal surface , assumed to be the x-y plane , a small trolley A is moving along a straight line parallel to the y-axis ( see figure) with a constant velocity of (sqrt(3)-1) m//s . At a particular instant , when the line OA makes an angle of 45(@) with the x - axis , a ball is thrown along the surface from the origin O . Its velocity makes an angle phi with the x -axis and it hits the trolley . (a) The motion of the ball is observed from the frame of the trolley . Calculate the angle theta made by the velocity vector of the ball with the x-axis in this frame . (b) Find the speed of the ball with respect to the surface , if phi = (4 theta )//(4) .

A body starts from rest from the origin with an acceleration of 3 m//s(2) along the x-axis and 4 m//s^(2) along the y-axis. Its distance from the origin after 2 s will be

A body starts from the origin with an acceleration of 6 ms^-1 along the x - axis and 8 ms^-1 along the y - axis. Find its distance from the origin after 4 s .

A body starts from rest from the origin with an acceleration of 6m//s^(2) along the x-axis and 8m//s^(2) along the y-axis. Its distance from the origin after 4 seconds will be

A body starts from rest from the origin with an acceleration of 6m//s^(2) along x axis and 8m//s^(2) along y axis.The distance from origin after 4 seconds will be

An object starts from rest at the origin and moves along the x axis with a constant acceleration of 4m//s^(2) . Its average velocity as it goes from x=2 m to x=8 m is :

A straight line makes an angle of 135^(@) with the X-axis and cuts Y-axis at a distance -5 from the origin. The equation of the line is

A straight line makes an angle with positive direction of x -axis measured in anti clock direction and makes positive intercept on y- axis and the line is at a distance of 5units from origin then its equation is

A particle starts from the origin with a velocity of 2cm/s and moves along a straight line.If the acceleration of the particle at a distance xcm from the origin be (2x-(3)/(2))(cm)/(s^(2)), find the velocity of the particle at a distance 7cm from the origin.