# Equations of Motion Under Gravity

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**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 |

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**(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.