IIT (NTSE/Olympiad)  

Motion in one Dimension

Points to Remember - Motion in One Dimension

1. If body starts from rest or falls freely or is dropped then, u = 0.
2. If the body is thrown upwards then it will rise until its vertical velocity becomes zero. Maximum height attained is h = u2/2g.
3. If air resistance is negligible then the time of the rise is equal to time of fall and each is equal to t = u/g.
4. The body returns to the starting point with the same speed with which it was thrown.
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 90º shows 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 v – t graph is a straight line parallel to time axis, then the acceleration of the body is zero.
10. If the graph is a straight line inclined to time axis with positive slope, then that body is moving with constant acceleration.
11. If v – t graph is a straight line inclined to time axis with negative slope, then the body is retarded.
12. Velocity and acceleration of a body need not be zero simultaneously.
13. A body in equilibrium has zero acceleration only. All other quantities need not be zero.
14. If a body travels with a uniform acceleration a1 for a time interval t1and with uniform acceleration a2 for a time interval t2, then the average acceleration a =
15. For a body moving with uniform acceleration, the average velocity (u + v)/2, where u is the initial velocity and v is the final velocity.
16. The distance travelled by the body in successive second 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 another body is projected horizontally from the same point, both will reach the ground at the same time.
19. If the v – t graph is a curve whose slope decreases with time then the acceleration goes on decreasing.
20. If the v-t graph is a curve whose slope increases with time then the acceleration of the body goes on increasing.
21. The v-t graph normal to time axis is not a practical possibility because it means that the acceleration of the body is infinite.

Various Graphs Related to Motion :
A. Displacement-Time Graph :
(a) For a stationary body

(b) For a body moving with constant velocity

(c) For a body moving with non-uniform velocity

(d) For a body with accelerated motion

(e) For a body with decelerated motion

(f) For a body which returns towards the point of reference

(g) For a body whose velocity constantly changes

(h) For a body whose velocity changes after certain interval of time

B. Velocity-Time Graph:
(a) For the body having constant velocity or zero acceleration

(b) When the body is moving with constant retardation and its initial velocity is not zero

(c) When body moves with non-uniform acceleration and its initial velocity is zero.

C. Acceleration-Time Graph :
(a) When acceleration is constant

(b) When initial acceleration is zero and rate of change of acceleration is non-uniform



IIT (Class X)

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