1. What Does Motion Under Gravity Mean?
Motion under gravity refers to the movement of an object when the only force acting on it is gravity. In such a case, the object accelerates downward with a constant acceleration \( g \) (approximately 9.8 m/s² on Earth).
This motion can be upward, downward, or vertical, and is described using the same kinematic equations you learned in linear motion—except that the acceleration is always \( g \), acting downward.
1.1. Why This Motion is Special
Gravity provides a uniform acceleration, meaning the object’s velocity changes at a constant rate. This allows us to predict and calculate the object's motion very accurately.
1.1.1. Everyday Examples
- A ball thrown upward
- A stone dropped from a height
- Raindrops falling from the sky
- An object tossed vertically
2. Kinematic Equations for Motion Under Gravity
We use the standard kinematic equations with acceleration \( a = g \). When taking upward direction as positive, gravity acts downward, so acceleration becomes \( -g \).
The equations are:
\( v = u + at \)
\( s = ut + \dfrac{1}{2}at^2 \)
\( v^2 = u^2 + 2as \)
Here, \( a \) is replaced by \( g \) or \( -g \), depending on the direction.
2.1. Sign Convention (Very Important)
- Upward motion: take upward as positive → \( a = -g \)
- Downward motion: take downward as positive → \( a = +g \)
3. Downward Motion (Object Dropped)
When an object is simply dropped, its initial velocity \( u = 0 \). Acceleration is \( +g \) if downward is taken as positive.
The equations simplify to:
\( v = gt \)
\( s = \dfrac{1}{2}gt^2 \)
\( v^2 = 2gs \)
3.1. Example
If you drop a stone from a height of 20 m, you can calculate how long it takes to fall or how fast it is moving after a certain time.
4. Upward Motion (Object Thrown Upwards)
When an object is thrown upwards, it moves against gravity. Its velocity decreases until it becomes zero at the highest point.
Here, acceleration is \( -g \).
\( v = u - gt \)
\( h = ut - \dfrac{1}{2}gt^2 \)
\( v^2 = u^2 - 2gh \)
At the maximum height, \( v = 0 \).
4.1. Important Observations
- The time taken to go up equals the time to come down (if the object returns to the starting point).
- The speed with which it returns is equal to the speed with which it was thrown.
5. Motion from Maximum Height (Fall After Reaching Top)
Once the object reaches its highest point, it momentarily stops before falling back under gravity. The downward motion follows the same equations as a simple free-fall.
5.1. Two-Stage Motion
The complete motion of a body thrown upward consists of:
- Upward motion with \( -g \)
- Downward motion with \( +g \)
6. Velocity-Time and Displacement-Time Graphs
Graphs help visualize motion under gravity.
6.1. Velocity-Time Graph
- Downward fall → straight line with positive slope (slope = g)
- Upward throw → straight line with negative slope (slope = -g)
6.2. Displacement-Time Graph
- Curved upward or downward depending on direction
- Parabolic shape as equations involve \( t^2 \)
7. Why Studying Motion Under Gravity Matters
The study of motion under gravity helps explain many physical phenomena such as falling objects, projectile motion, and vertical motion. It is essential for understanding sports physics, engineering, planetary motion, and even rocket launches.
In the next topic, we study the special case of motion under gravity called free fall, where gravity is the only force acting on an object.