Equations of Motion Under Gravity : : Motion in One Dimension
|i. v = u + at
ii. h = ut + 1 / 2 gt^2
iii. v^2 – u^2 + 2gh
(b) Upward Motion :
|(i) v = u – at
(ii) h = ut – 1 / 2 gt^2
(iii) v^2 – u^2 – 2gh
(c) In general condition :
|(i) v = u + at
(ii) h = ut + 1 / 2 at^2
(iii) v^2 – u^2 + 2as
(d) Distance traveled by a body in the second :
|snth = u + ( 2n – 1 ) a / 2|
- where, s = distance traveled, h = height, t = time, u = initial velocity, v = final velocity, a = acceleration, g = gravitational acceleration.
- If rain drops are falling vertically with a velocity v and a person is walking horizontally with a velocity u, then he should hold and umbrella at an angle θ with vertical given by tan θ = u/v to prevent himself from being wet.
Memorable Points :
- If a body starts from rest and falls freely or is dropped, then u = 0.
- If the body is thrown upwards then it will rise until its vertical velocity becomes zero. Maximum height attained is h = u2 /2g.
- If a packet is dropped at a height h, from an aero-plane or balloon ascending with a velocity u, then the time taken by the packet to reach ground is given by h = ut + 1/2 gt^2.
- No line in x – t graph can be perpendicular to time axis because it will represent infinite velocity.
- 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.
- If the x – t graph is a curve whose slope continuously increases, then the velocity of the body is continuously increasing and the body accelerated.
- If the v – t graph is a straight line parallel to time axis, then the acceleration of the body is zero.
- If the u – t graph is a straight line inclined to time axis with positive slope, then that body is moving with constant acceleration.
- If v – t graph is a straight line inclined to time axis with negative slope, then the body is retarded.
- The v – t graph normal to time axis is not a practical possibility because it means that the acceleration of the body is infinite.
- 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.
- The distance traveled by the body in successive seconds is in the ratio 1:3:5:7…..etc.
- When the body is starting from rest, the distances traveled 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.
- 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.
Application Form Submission 16 Dec 2020 to 16 Jan 2021.