MOTION IN ONE DIMENSION

1-Rest & motion are relative terms.

2-There is no meaning of rest or motion without the viewer.

3-Nothing is in absolute rest or in absolute motion.

4-For a moving object distance can never decrease with time. Thus for a moving object the (distance/time) curve is strictly increasing.

5-Magnitude of displacement vector between two points is the shortest distance between these two points. Hence:-|displacement| ≤ distance

6-For a moving particle distance can never decreases with time while displacement can.

  • Decrease in displacement means body is moving towards the initial position.

7-The instantaneous velocity is always tangential to the path followed by the particle. Hence:-|instantaneous velocity|= instantaneous speed

8-Velocity remain constant throughout a given interval of time, the motion is said to be uniform & for uniform motion. V=constant=V(av)

  • However converse may not be true.

9-Velocity is constant, speed ( =|velocity| ) will also be constant. However converse may not be true.

10-For a given interval average velocity is singled valued, while average speed can have many values depending on path followed.

11-For a moving body average speed can never be negative or zero (unless t~infinity), while average velocity can be i.e. V(av) > 0 while v̅ (av) >= or < 0

12-Since |displacement| ≤ distance, hence |average velocity| ≤ average speed i.e. Magnitude of average velocity is always less than or equal to average speed for same interval of time.

13:-If a particle is moving with uniform acceleration, this doesn’t necessarily imply that particle is moving in straight line.

14:-There is no definite relationship between the direction of velocity vector & direction of acceleration vector.

  • Angle between them may have any value.

15:-If a body is acted upon by a constant acceleration, it’s path 

  • Will be staraigh line if it’s initial velocity is along the line of acceleration 
  • Will be a parabola if it’s initial velocity is making some angle other than zero or 180° with the acceleration.

16:-If an object is moving along a straight line, it’s acceleration vector is along the line of motion.

17:-In general, the path followed by a particle maybe curved. Then net acceleration of the particle has two components.

18:-Tangential acceleration is the rate of change of speed i.e.{ a=d|v̅|/dt }

  • Normal acceleration = V^2/r
  • Where v= speed of particle ; r= radius of curvature of the path.

19:-For a body moving with uniform acceleration, we have average acceleration = instantaneous acceleration.

       THE SLOPE OF MOTION GRAPHS

                            FIGURE:-A                  

                     MOTION GRAPHS

                            FIGURE:-B

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