Equations of Motion Under Gravity: Derivation, Uses & Common Mistakes
Motion under gravity is a JEE Main fundamental describing how objects behave when the only force acting is gravity. This concept helps students analyze free fall, vertical throws, and real-life scenarios like falling objects or upward-projected balls. Understanding motion under gravity is crucial for kinematics, projectile motion, and gravitation chapters, making it a scoring topic in JEE Physics.
In such cases, the acceleration remains constant and is equal to the acceleration due to gravity (symbol g). On Earth, g is approximately 9.8 m/s2 downward. JEE questions frequently require applying specific formulas and recognizing the type of vertical motion involved. You may also need to distinguish between general motion equations and those used for motion under gravity.
Every JEE aspirant should master applying kinematics in the context of gravity. Also, be familiar with essential variants such as vertical motion under gravity, free fall equations, and how they differ from general motion.
Definition and Physical Meaning of Motion Under Gravity
When an object moves in a straight line under the influence of gravity alone, we call it motion under gravity. This applies when air resistance is negligible, such as a freely falling stone or an object thrown vertically upwards. The constant acceleration here is always directed downward, with magnitude g.
Studying this concept builds the foundation for later topics like projectile motion and advanced kinematics. Questions in the exam often expect you to model such vertical motion, solve for displacement, or determine final velocities.
Main Equations for Motion Under Gravity
The core equations are derived from standard equations of motion, setting acceleration a = -g (downwards, usually negative if upward is positive). For JEE, always define your sign convention at the start. Common symbols used:
- u: Initial velocity (upward or downward)
- v: Final velocity after time t
- g: Acceleration due to gravity (9.8 m/s2)
- t: Time elapsed
- s: Vertical displacement
| Equation | Name / Use |
|---|---|
| v = u + gt | Velocity after time t |
| s = ut + ½gt2 | Vertical displacement in time t |
| v2 = u2 + 2gs | Relates velocity and displacement |
When solving numericals, keep a consistent direction. Assign g as positive downward or negative upward and stick with it. Mistakes in sign convention are frequent exam traps.
For further details on acceleration due to gravity and its derivation, refer to the linked concepts.
Types of Motion Under Gravity: Free Fall vs. Upward Throw
JEE Main questions use two main types of vertical motion under gravity:
- Free fall: Object is dropped (u = 0) and accelerates downward.
- Upward throw: Object is projected upwards (u > 0), slows down, stops at maximum height, then descends.
| Case | Initial Velocity, u | Acceleration, a | Direction of g |
|---|---|---|---|
| Free Fall | 0 | +g (down) | Downward |
| Upward Throw | >0 (Up) | -g (up) | Always downward |
Note: On the way up, gravity slows the object. At max height, velocity is zero. On the way down, gravity increases the speed. Both motions use the same set of equations but with different signs for u and g as per your chosen convention.
Compare this formalism to general motion equations in one dimension. The difference is that motion under gravity always sets acceleration to the specific value of g.
Worked Example: Motion Under Gravity Numericals
Let’s solve a classic JEE-style motion under gravity problem:
- A ball is thrown vertically upward from the ground with u = 20 m/s.
- g = 9.8 m/s2 (downward is negative, so take g = -9.8).
- Find maximum height reached (v = 0 at top).
- Using v2 = u2 + 2gs, set v=0.
- 0 = (20)2 + 2(-9.8)s ⇒ s = (400)/(19.6) = 20.4 m.
Thus, the ball rises to a maximum height of 20.4 m. Always justify sign usage on each term.
For additional solved questions, see the page for motion under gravity numericals and kinematics practice paper.
Applications, Common Pitfalls, and JEE Tips
Motion under gravity appears in many real-life and exam contexts:
- Finding time of flight for vertically projected objects
- Calculating velocity just before hitting the ground
- Comparing free fall and thrown motions
- Error in sign convention or positive/negative g
- Ignoring air resistance except when specified
- Assuming g is always 9.8; be aware of location specifics
JEE frequently tests conceptual traps like total time in the air, handling objects thrown from heights or in elevator cases, and the difference between free fall and projectile motion. For deeper insight, consult laws of motion and gravitation fundamentals.
Common mistakes include mixing direction signs, misusing initial conditions, or skipping unit checks. Always stick to a single axis and consistent direction for “up” and “down.”
Graphical understanding is aided by the velocity-time graphs for motion under gravity and kinematic graphical analysis.
For reference, if asked about vertical motion under gravity versus projectile motion, remember that projectile motion has horizontal and vertical components, while pure motion under gravity is in one dimension.
This concept is also the foundation for time-of-flight calculations and energy conservation in later JEE Physics problems. Reviewing work, energy, and power laws will strengthen your mastery.
In summary, motion under gravity is a scoring area in JEE Main. Mastery means careful sign convention, correct equation selection, and regular problem-solving practice. For in-depth revision and practice, explore the related Vedantu resources linked throughout this guide.
FAQs on Motion Under Gravity: Definition, Formulas, Applications & Numericals
1. What is motion under gravity?
Motion under gravity refers to the movement of an object when only the force of gravity is acting on it, with no other external forces. Key points include:
- Examples are a stone dropped from a height or a ball thrown upwards.
- This motion can be free fall or vertical throw.
- The acceleration is always g (acceleration due to gravity) toward Earth's center.
- Relevant for JEE, NEET, and Class 11 Physics exams.
2. What are the equations of motion under gravity?
The equations of motion under gravity are the kinematics formulas adjusted to include gravitational acceleration (g):
- v = u + gt
- s = ut + ½gt²
- v² = u² + 2gs
u = initial velocity, v = final velocity, s = displacement, t = time, and g = acceleration due to gravity (9.8 m/s² downward).
3. Is motion under gravity always free fall?
Motion under gravity is not always free fall. Free fall specifically means an object moves only under gravity with zero initial velocity.
- If an object is projected upward or downward, it still experiences motion under gravity but not free fall.
- Free fall is a special case where only gravity acts, with no initial upward velocity.
4. What is the motion of a ball under gravity?
When a ball moves under gravity, it accelerates towards the Earth at g = 9.8 m/s². Depending on its initial velocity:
- If dropped: it accelerates down, increasing speed uniformly.
- If thrown upward: it slows down, stops momentarily, then accelerates downwards.
- The equations of motion under gravity apply for both cases.
5. What is the value of ‘g’ on Earth?
On Earth, the acceleration due to gravity, g, is approximately 9.8 m/s² directed towards the center of the planet. This value:
- Varies slightly with altitude and latitude.
- Is rounded to 10 m/s² for quick calculations in exams.
- Is a constant used in all motion under gravity formulae.
6. What is motion under gravity formula?
The key formulae for motion under gravity are adapted kinematic equations using g (gravity):
- v = u + gt
- s = ut + ½gt²
- v² = u² + 2gs
7. What is free fall motion?
Free fall motion is when an object moves only under the influence of gravity, with no other forces acting on it, often starting from rest. Characteristics include:
- Acceleration is g downwards.
- Initial velocity (u) is zero unless otherwise specified.
- All objects (ignoring air resistance) fall at the same rate regardless of mass.
8. Why do all objects accelerate equally under gravity?
All objects accelerate equally under gravity because the acceleration due to gravity (g) is independent of mass. Key reasons:
- Gravity exerts a force proportional to mass, but acceleration (F/m) cancels mass out.
- As a result, heavy and light objects experience the same acceleration if air resistance is ignored.
- This principle was proven by Galileo and is a foundation of classical mechanics.
9. What changes if the initial velocity is upwards?
If an object's initial velocity is upwards under gravity:
- It will slow down until its velocity becomes zero at the highest point.
- After reaching the peak, it accelerates downward due to gravity.
- The motion is divided into upward (decelerating) and downward (accelerating) phases, both using the same equations with appropriate signs for u and g.
10. What are some common mistakes in solving motion under gravity numericals?
Some common mistakes in motion under gravity problems include:
- Using incorrect sign conventions for g (positive or negative depending on upward or downward motion).
- Confusing initial velocity (u) and final velocity (v) in calculations.
- Not carefully reading whether an object is thrown or dropped.
- Ignoring air resistance when required in practical contexts.
- Mixing up upward and downward motion formulas.
