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Kinematics

Kinematics. KINEMATICS. STATICS is the study of the motion of an object under the effect of forces in equilibrium… KINEMATICS is the study of the motion of the objects without taking into account the cause of their motion...

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Kinematics

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  1. Kinematics

  2. KINEMATICS STATICS is the study of the motion of an object under the effect of forces in equilibrium… KINEMATICS is the study of the motion of the objects without taking into account the cause of their motion... DYNAMICS is the study of the motion of the objects by taking into account the cause of their motion... introduction

  3. POSITION-TIME GRAPH (UNIFORM MOTION) Position-time graph for an object in uniform motion along a straight path is a straight line inclined to the time axis... The velocity of uniform motion is equal to the slope of position-time graph... POSITION(m) TIME(s)

  4. VELOCITY-TIME GRAPH (UNIFORM MOTION) Displacement of an object in time interval is numerically equal to the area under velocity-time graph between the instants... velocity time

  5. UNIFORMLY ACCELERATED MOTION IN A STRAIGHT LINE The motion of an object is said to be uniformly accelerated ,if the same change in its velocity takes place in each unit of time… Average speed is defined as the ratio of the path length to the time taken by the object to cover that path… AVERAGE SPEED OF UNIFORM MOTION=(Path length)/(time interval)… Average velocity is defined as the ratio of the displacement to the time taken by the object to cover that displacement…. AVERAGE VELOCITY OF THE UNIFORM MOTION = (Displacement)/(time interval). The average velocity of an object is a vector quantity.

  6. Rest And Motion An object is said to be in motion , if it changes its position with respect to its surroundings with the passage of time. EXAMPLES:- An airplane or a bird flying through the air A ball thrown by a girl A ship sailing on a sea If the object doesn’t change its position with respect to its surroundings with the passage of time, it is said to be at rest. Sometimes the objects are in motion but the motion may not be visible to us. For example , a gas molecules are always in ceaseless random motion , though their motion is not visible to the naked eye.

  7. Uniform motion in a straight line UNIFORM MOTION:- The motion of an object is said to be uniform, if it covers equal displacements in equal interval of time. UNIFORM SPEED:- It is defined as the ratio of the path length to the time taken by the object to cover that path. Speed of the uniform motion = (path length)/(time interval) UNIFORM VELOCITY:-It is defined as the ratio of displacement to the time taken by the object to cover that displacement. Velocity of the uniform motion =(displacement)/(time interval) AT t=0 AT t=t AT t=t’ X O A B X V=(x’-x)/(t’-t) X’

  8. Expression for displacement V=(x’-x)/(t’-t) x’-x=v(t’-t) x’=x + v(t’-t) AT t=0 AT t=t X O A B xo x x = x0 +v(t’-0) x = xo + vt x – x0 =vt If x-xo=S, the displacement of the object in time t, then the equation becomes S=vt

  9. Velocity Time Relation a = acceleration due to gravity a = (v’-v)/(t’-t) v’ = v + a(t’-t) This equation is velocity time relation, which gives the velocity of an object at any time t and the uniform acceleration a of the object. a = (v-u)/(t-0) =(v-u)/t v =u + at

  10. Questions A body travels from A to B at 40m/s and from B to A at 60m/s. Calculate the average speed and average velocity? Ans:- let t1and t2 be time in seconds taken by the body to go from A to B and then from B to A respectively. Then, t1 + t2 = AB/40 + BA/60 = AB(1/40 +1/60) = AB/24s Total distance covered = AB + BA = 2AB Average speed = 2AB/t1+t2 =2AB /AB/24 = 48m/s Since the body reaches the starting position, the net displacement is o. Therefore, Average velocity = displacement/time =0/AB/24 = 0

  11. Position-time graph for two objects moving with equal velocities For object P’ Position(m) For object P Time(s) Thus position time graph for 2 objects P and P’ moving with equal velocity along a straight path will be the two parallel lines.

  12. POSITION TIME GRAPH FOR TWO OBJECTS MOVING WITH UNEQUAL VELOCITIES Position of meeting For object P For object P’ position Time of meeting time Thus, if 2 objects move with unequal velocities ,then the position time graph will be straight lines inclined to time axis and intersect each other. If the velocities of the 2 objects are of opposite signs, then the magnitude of their relative velocity v’-v is greater than the magnitudes of both v and v’.

  13. Thank You

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