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Motion Equations Of Motion Speed Vs Velocity Visualize Motion
Have you ever found yourself staring at the three equations of motion, wondering where they came from and how to use them? You’re not alone.
Many students memorize these equations without truly understanding them. In class tests or board exams, a small twist in the question-like a missing variable or a different unit-can throw everything off. Instead of applying the equation logically, most students panic and either guess or get stuck.
So, what’s going wrong?
Most often, the issue is with the foundation. Students know the formulas, but not the "why" behind them.
Let’s be honest-physics is not a subject you can just memorize and score high in. It demands understanding.
If you’ve ever tried to solve a motion-related problem like:
“A car accelerates from rest at 2 m/s². What is its velocity after 5 seconds?”
You may rush to pick the formula without even checking if it's the right one. Or worse, you forget the signs, misplace units, or use the wrong variables altogether.
In the long run, these small mistakes snowball. They affect not just your grades but also your confidence. And if you plan to go into engineering, mechanics, aviation, sports science, or any field involving physical systems-you’ll face this topic again.
So, let's stop memorizing and start understanding.
We’ll approach this as if you’re learning it for the first time-but the right way. No skipping steps. No fancy jargon. Just logic, reasoning, and practical application.
The three fundamental equations of motion are:
Where:
Let’s derive each one.
Derivation of Equation 1: v = u + at
We start from the definition of acceleration:
Acceleration (a) = Change in velocity / Time taken
=> a = (v - u) / t
=> at = v - u
=> v = u + at
Done. Simple logic. This equation tells us how velocity changes over time under uniform acceleration.
Derivation of Equation 2: s = ut + ½at²
Let’s find the distance travelled in time t.
We use this idea:
Displacement = Average velocity × Time
Average velocity (under constant acceleration) = (u + v)/2
From the first equation, we know v = u + at
So,
s = [(u + v)/2] × t
= [(u + (u + at)) / 2] × t
= [(2u + at)/2] × t
= ut + ½at²
That’s our second equation.
Derivation of Equation 3: v² = u² + 2as
Let’s eliminate time from the equations.
We know:
v = u + at
s = ut + ½at²
From the first:
t = (v - u)/a
Substitute into the second:
s = u × (v - u)/a + ½a × [(v - u)/a]²
After simplifying:
v² = u² + 2as
You don’t need to memorize this derivation—but understanding how one leads to the next helps you see the big picture.
Now that we’ve derived the equations, let’s see how to apply them.
Each equation is best suited for situations when:
| Equation | Use When... |
| v = u + at | You don’t need displacement |
| s = ut + ½at² | You don’t know final velocity |
| v² = u² + 2as | You don’t know time |
A simple way to remember this is by checking what values are missing from the question. Use the formula that doesn’t involve the missing value.
Let’s say a car moving at 20 m/s comes to a stop with uniform deceleration of 4 m/s².
How far will it travel before stopping?
Given:
u = 20 m/s
v = 0 m/s (since it stops)
a = -4 m/s²
s = ?
use:
v² = u² + 2as
0² = 20² + 2×(-4)×s
0 = 400 - 8s
8s = 400
s = 50 meters
Answer: The car stops in 50 meters.
An object is dropped from a building. How far does it fall in 3 seconds?
Given:
u = 0 (starts from rest)
a = 9.8 m/s² (acceleration due to gravity)
t = 3 s
s = ?
Use:
s = ut + ½at²
= 0 + ½ × 9.8 × 3²
= 0.5 × 9.8 × 9
= 44.1 meters
Answer: The object falls 44.1 meters in 3 seconds.
Imagine you're riding your bike and you increase your speed from 5 m/s to 15 m/s in 10 seconds. What is your acceleration?
Given:
u = 5 m/s
v = 15 m/s
t = 10 s
a = ?
Use:
v = u + at
=> 15 = 5 + 10a
=> 10a = 10
=> a = 1 m/s²
You’re accelerating at 1 m/s²-meaning each second your speed increases by 1 m/s.
1. Wrong sign conventions
Always take one direction as positive (usually upward or rightward). For free fall, acceleration due to gravity is +9.8 m/s² downward, and -9.8 m/s² if upward is taken positive.
2. Mixing up units
Ensure time is in seconds, velocity in m/s, and acceleration in m/s².
3. Using the wrong equation
Don’t just plug in numbers. Pause, look at what is given and what is missing. Pick the right formula accordingly.
4. Assuming motion is always starting from rest
Unless mentioned, never assume u = 0. It may be any value.
These equations are not just for school exams.
1. Automotive Engineering:
Used to calculate acceleration, stopping distances, crash simulations.
2. Sports Science:
To analyze performance in running, cycling, jumping, and throwing.
3. Space Science:
To track trajectories, rocket launches, and satellite motion.
4. Civil Engineering:
To predict the fall time of debris, elevator motion, and slope safety.
5. Safety Design:
To develop airbags, brake systems, and barriers using motion analysis.
Mastering this topic gives you an edge-not just in physics class but in understanding how the world works.
Try solving these:
Understanding the equations of motion is not just about scoring in exams. It’s about being able to analyze any moving object around you-be it a cricket ball, a speeding car, or your own sprint.
By deriving the equations, knowing when to use each, and applying them through relatable examples, you can transform this chapter from a headache to your strong point.
So next time you see a motion question, don’t panic. Ask:
If you want to practice this topic, you can take a quiz in Curious Corner for better practice.
*Note: You must register yourself to access the quizzes.*
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