Motion Topics Introduction to Equation of Motion Equation for Velocity Time Relation Equation for Position Time Relation Equation for Position Velocity Relation Learning Objectives:

Motion Introduction to Equations of Motion When an object moves along a straight line with uniform acceleration, then relation between velocity, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion.

Motion There are three such equations: Where u is the initial velocity of the object which moves with uniform acceleration ‘a’ for time t, v is the final velocity, and ‘s’ is the distance traveled by the object in time ‘t’. These three equations can be derived by graphical method. Introduction to Equations of Motion

Motion Equation for Velocity-Time Relation Consider the velocity-time graph of an object that moves under uniform acceleration. Suppose an object moving with initial velocity OA=u, And its final velocity is BC=v change in velocity BD=BC – CD time is OC=t.

Motion Equation for Velocity-Time Relation

Motion Equation for Position-Time Relation Let us consider that the object has travelled a distance ‘s’ in time t under uniform acceleration ‘a’. The distance travelled by the object is obtained by the area enclosed within OABC under the velocity-time graph AB. Area OABC of trapezium = area of the rectangle OADC + area of the triangle ABD

Motion Equation for Position-Time Relation

Motion Equation for Position–Velocity Relation The distance ‘s’ travelled by the object in time t, moving under uniform acceleration ‘a’ is given by the area enclosed within the trapezium OABC under the graph. That is, s = area of the trapezium OABC

Motion Equation for Position–Velocity Relation Substituting OA=u, BC = v and OC = t, we get

Motion Equation for Position–Velocity Relation From the velocity time relation we get Using Eqs. and we have