Ž : In component form, we have : a where, a dv dt , a dv dt , a dv dt . If an object is moving in a plane with constant acceleration and its position vector at time t = is r o , then at any other time t , it will be at a point given by: and its velocity is given by : v = v o + a t where v o is the velocity at time t = In component form : ox v t oy ox oy Motion in a plane can be treated as superposition of two separate simultaneous one- dimensional motions along two perpendicular directions . An object that is in flight after being projected is called a projectile . If an object is projected with initial velocity v o making an angle θ o with x- axis and if we assume its initial position to coincide with the origin of the coordinate system, then the position and velocity of the projectile at time t are given by : x = ( v o cos θ o ) t y = ( v o sin θ o ) t − ( / ) g t v x = v ox = v o cos θ o v y = v o sin θ o − g t The path of a projectile is parabolic and is given by : cos gx x – v The maximum height that a projectile attains is : h 2g = ( q The time taken to reach this height is : The horizontal distance travelled by a projectile from its initial position to the position it passes y = during its fall is called the range , R of the projectile.
It is : sin2 . When an object follows a circular path at constant speed, the motion of the object is called uniform circular motion . The magnitude of its acceleration is a c = v /R . The direction of a c is always towards the centre