MOTION IN ONE DIMENSION

Equations of motion

These equations describe relation between initial velocity (u), final velocity (v), displacement(s), time (t) and acceleration (a), for uniformly accelerated motion.                        

 

First equation

 v = u+at

Second equation

s= ut+ at²

Third equation

 v ²- u² =2as

 

Distance traveled in nth second (S_n) is the distance traveled in one second between t = n and t = n-1 seconds

S_n=u +  (2n-1)

 

                                            PROJECTILE MOTION

For a body projected with initial velocity ‘u’ at an angle ‘’ with the horizontal

                                                     

 

Equation of trajectory: y=

 

Time of flight =

Maximum height =

Range =

Horizontal component velocity at time‘t’ = v_x=

 

Vertical component velocity at time‘t’ = v_y=

 

Velocity at time‘t’ = =

 

Angle made by velocity with horizontal = =tan^-1 = tan^-1

Position at time‘t’: x = (u cos) t, y = (u sin) t -g t²

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