 # Important formulas of Kinematics

• Average Speed = • If the body covers 1st half of distance with a speed x and the second half with a speed y,then the average speed = • If the body covers 1st 1/3rd of a distance with a speed x , and 2nd 1/3 with a speed y , and the 3rd 1/3rd distance with a speed z, then average speed = • Average velocity = • If a body travels a displacement in seconds and a displacement in seconds, in the same direction then   Average velocity = .
• If a body travels a displacement with velocity , and displacement with velocity in the same direction then Average velocity = • If a body travels first half of the displacement with a velocity and next half of the displacement with a velocity in the same direction , then                                                          Average velocity = .
• If a body travels a time with velocity and for a time with a velocity in the same direction then Average velocity = .
• If the body travels 1st half of the time with a velocity next half of the time with a velocity in same direction , then  Average velocity = • For a body moving with uniform acceleration if the velocity changes from u to v in t seconds, then Average velocity = (u+v)/2 .

• Equations of motion of a body moving with uniform acceleration along straight line.
• a) V=u+at    b) S=ut+  c)  =2as
• Distance traveled  in the nth second =u+a(n-1/2)
• Equations of motion for a freely falling body ( Note: we can obtain these equations by substitution of u=0 and a=g in above equations . a) v=gt b) S=1/2 c) = 2gs and the equation for the distance traveled in nth second changes to =g(n-1/2)
• Equations of motion of a body projected up vertically :(we will obtain these equations by substitution a=-g in equations of motion)
• a) v=u-gt  b) S=ut-1/2 c) =-2gs and =u-g(n-1/2)
• Equation for maximum height reached =   • Time of ascent = ;  u
• Time of descent =   u
• Time of flight T=2u/g
• When a body is thrown up from top of a tower or released from a rising baloon,with velocity u.Displacement traveled before reaching ground              S=-ut+1/2 . (t= time during which the object is in the air and S=h=height of the tower).
• When a body is dropped from a tower of height h and another body is thrown up vertically with a velocity u then they will meet after t=h/u seconds.
• When a body is dropped from a tower of height h . Its velocity when it reaches ground v= • If the displacements of a body in seconds of its journey.Then the uniform acceleration of the body a= • From the above equation we can observe that by substituting n=1,2,3,4,…. we get a= = =……….. = =a.
• A body projected up with velocity u from the top  of a tower reaches ground in seconds.If  it  is thrown down with the same velocity u it reaches ground in seconds.Then, when it is dropped freely the time taken to reach the ground will be t= and h=1/2 g and =2 .
• Projectile motion :Let us suppose that a projectile is projected with an initial velocity u making an angle with x axis. a)Horizontal component of velocity , and ,which will be constant through out the flight of the projectile as horizontal component of acceleration = 0.  b)Vertical component of velocity of the projectile . Vertical component of velocity at any time of its journey = -gt or = -gt.   c)Magnitude of the resultant velocity V = and the angle x made by v with the horizontal is given by = • Time of ascent = • Time of descent = • Time of flight = • Maximum height reached = ; = when u is same
• Horizontal Range R= = a)R is maximum when = b) = c) If T is the time of flight, R= d)For given velocity of projection R is same for the angles of projections and Ex: 25 and 65 i.e the Range for those two angles will be same whose sum is )