One Dimensional Motion

One Dimensional Motion


On the Horizontal Straight Line Path:

Rest and motion are relative.

* The shortest distance between initial and final positions of a moving particle is its displacement. Displacement is a vector quantity, while distance is a scalar.


* A body can have distance without displacement.
Ex : When a particle completes one rotation, its distance is 2r and displacement is zero


* A particle moves along the circumference of a circle of radius 'r'. If the angle made by the radius vector at the centre is , then
(a) displacement = 2 r sin
(b) distance travels = r


* Speed is defined as the rate of change of distance travelled by a particle with respect to time. It is a scalar.


* Average speed =


* Displacement in unit time is Velocity. It is a vector quantity


* A body along a straight line, travelled equal displacements with velocities v₁,v₂,v₃ ......, then average velocity V =



Note:- Distance is always positive. Displacement may be positive, negative or zero.


* Instantaneous velocity: the velocity of a particle at a given instant of time is called the instantaneous velocity instantaneous velocity


* Change in velocity = magnitude of change in velocity =


* When a body is with a constant velocity v in two directions making an angle , change in velocity = 2V sin ( )


* Rate of change of velocity of a particle with respect to time is acceleration. It is a vector. Acceleration is caused when there is a change in the Velocity.


* Equations of motion for a particle moving with uniform acceleration along a straight line.
a) V = u + at
b) S = ut + 1/2 at²
c) V² – u² = 2as
d)


* Displacement of the particle in the nth second is



B. On the Vertical Straight Line Path:

* For a particle projected vertically up or falling downwards, if the distance travelled is negligible when compared to the radius of the earth; the acceleration due to gravity at a particular place can be taken constant g is slightly more at the poles of the earth than at the equator. Average value of g near the surface of the earth is 9.8 ms^-2 or 32 ft s^-2 or 980 cms^-2 Acceleration due to gravity is independent of mass. For a particle projected up; g is conventionally taken negative and positive if it is falling.


* 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 particle projected vertically up from the top of a tower takes t_i see to reach the ground. Another particle thrown downwards with the same velocity from the top of the tower takes. t₂ seconds to reach the ground. If the particle is dropped from the top of the tower, time taken is

i)

ii) height of the tower is h = gt₁t₂

iii) Velocity of projection is u = (t₁-t₂)


* 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