Motion in one Dimension

Distance      ≥ 1 ;   speed   ≥ 1.
Displacement            Velocity
1.  If a body moves certain distance with speed V1 and returns to same point with speed V2 then,Average speed; (V) = 

2V₁V₂

V₁+V₂

If a person moves with equal distances with speed V₁, V₂, V₃ and so on them average speed (n/v) = 1/ V₁ + 1/ V₂ +1/ V₃..................+ 1/ V_n

Average speed (V) = H.M. of V₁, V₂, V₃, ……… V_n

2.  If a body moves with different speed V₁, V₂, V₃, ……… Vn in equal time interval then,

Average speed (V) =

V₁+ V₂+ V₂+...................+ V_n

                         n

  = A.M.

3.  Equation of kinematics are applicable for constant acceleration. i.e. when acceleration. i.e. when acceleration is not varying with time.

4.  If the x – t graph is a straight line parallel to axis then the body is at rest.
5.  The straight line inclined to time axis in x-t graph represents constant velocity.

6.  In x-t graph the straight line inclined to time axis at an angle greater than 90°, show negative velocity.
7.  No line in x-t graph can be perpendicular to time axis because it will represent infinite velocity.
8.  If the x-t graph is a curve whose slope decreases continuously with time,then the velocity of the body goes on decreasing continuously and the motion of the body is retarded.

9. If the x-t graph is a curve whose slope continuously increases,then the velocity of the body is continuously increasing and the body is accelerated.

10. If v-t the graph is a st. line parallel to time axis, then the acceleration of the body is zero (0).
11. If the v-t graph is a straight line inclined to time axis with positive slope, then that body is moving with constant acceleration.

12. If the v-t graph is a straight line inclined to time axis with negative slope, then the body is retarded.
13. The velocity and acceleration of a body need not be in same direction.

14. The velocity and acceleration of a body need not be zero simultaneously.

15. A body in equilibrium has zero acceleration only. All other quantities need not be zero.

16. The distance traveled by the body in successive seconds is in the ratio 1 : 3 : 5 : 7 ……………etc.
17. When the body is starting from rest, the distances travelled by the body in the first second, first two seconds, first three seconds,…………. etc. are in the ratio of 1 : 4 : 9 : 16 : 25 …………. etc.
18. When a body is dropped freely from the top of the tower and body is projected horizontally from the same point, both will reach the ground at the same time.

19. If the velocity–time graph is a curve whose slope decreases with time, the acceleration of the body goes on increasing.

20. If the particles starts from rest and the distance covered by it in time be s, then
i. If s α t, the acceleration is zero.

ii. If s α t², the acceleration is constant.

iii. If s α t², the acceleration is varies as the time (a α t).

21. If the distance covered (s) by a particle is proportional to t^3/2, then the power dissipated by it is constant.

22. If makes certain angle with then the path of the particle is a parabola.

23. Speed is always a positive quantity, however it may increase or decrease with time.

24. for uniform motion:

(a) Distance covered = magnitude of displacement;

(b) The motion is along a straight line;

(c) Direction of motion does not change.

Relative Motion :

1. If two bodies are moving in same direction then

 

2. If two bodies are moving in opposite direction then

3. If two bodies are moving perpendicularly then,

4. If rain drops are falling vertically with a velocity v and a person is walking horizontally with a velocity u, then he should hold an umbrella at an angle θ with vertical given by tanθ = u/v , to prevent himself from being wet.

5. A boat moving with a velocity v in still water crosses a river which is following with a velocity u, then:

i. To reach the opposite bank in minimum time, the boat must move at right angles to the current and time taken to cross the river. t = D/v , where D is width of river.

ii. To go straight across to the opposite bank, the boat must move at an angle θ = sin^-1(u/v) with the vertical or [90° + sin^-1(u/v)] with the direction of current and time.