One dimensional Motion

One dimensional Motion (xi) Speed Average speed Instantaneous speed Acceleration Average acceleration Instantaneous acceleration Equations of Kinematics a) V = u + at b) S = ut + 1/2 at2 c) V2 - u2 = 2as d)  Displacement of the particle in the nth second is For a particle projected up; g is conventionaly taken negative and positive if it is falling, u = 0 a) Velocity attained after falling for a time 't' is V = gt b) Distance fallen in a time t is h = gt2 c) Time taken to fall a distance h is  d) Velocity attained after falling a distance h is  e) Distance travelled in the nth sec, is Sn= (2n-1) If a body is thrown downward with a velocity u. Equations of motion are : a) V = u + gt b) v2- u2 = 2gh c) h = ut + gt2 d) Sn = u + (2n-1) If a particle is projected vertically up with a velocity U, acceleration is a = - g, Equation of motion are a) h = ut - gt2 b) v = u - gt c) v2 - u2 = -2gh d) Sn = u - (2n-1) for maximum height v = 0, (a) Hmax =  (b) t =  I u =  If an object is dropped from a ballon rising up with a velocity u at a height h. (i) Equation of motion relative to earth is h = - ut + gt2 ii) Equation of motion relative to ballon is h = gt2 If a body is projected vertically up with a velocity u from a tower and it reaches the ground with a relative nu., the height of the tower is . A elevator is accelerating upwards with an acceleration a. If a person inside the elevator throws a particle vertically up with a velocity u relative to the elevator, time of flight is  In the above case if elevator accelerates down, time of flight is   If a body is projected with a velocity u at an angle q to the horizontal. Projectile (XI) Vertical displacement at any time t. y = (u sin ) t - 1/2 gt2 Vertical component of velocity Vy = u sin  - gt. Equation of trajectory y = x tan  -  Time taken to reach the maximum height t =  Maximum height attained Hmax =  Time of flight T =  Range R =  Rmax =  tan  =  R = 1/2 g L1 L2 If R is maximum, Hmax = R/4. If R = Hmax,  = tan -1 (4)  760. (P.E.) = 1/2 mu2 sin . (K.E.) = 1/2 mu2 cos2. Horizontal projectile  Position after time t:  Horizontal displacement after time t. x = ut Distance fallen in time "t" y = gt2 Equation of path . Time of flight T =  Horizontal Range R =