What is the First Equation of Motion?

S6-SA3-0013

Grade Level:

Class 10

AI/ML, Physics, Biotechnology, Space Technology, Chemistry, Engineering, Medicine

Definition

What is it?

The First Equation of Motion helps us understand how the speed of an object changes over time when it moves with a constant acceleration. It links an object's initial speed, final speed, acceleration, and the time taken for the change.

Simple Example

Quick Example

Imagine you are riding your bicycle. You start from a stand-still (initial speed = 0). You pedal hard and after 5 seconds, your bicycle is moving at 10 km/hr (final speed). The First Equation of Motion helps us calculate how much you accelerated during those 5 seconds.

Worked Example

Step-by-Step

QUESTION: A scooter starts from rest and accelerates uniformly at 2 m/s^2 for 10 seconds. What will be its final speed?

---1. Identify the given values:
Initial speed (u) = 0 m/s (since it starts from rest)
Acceleration (a) = 2 m/s^2
Time (t) = 10 s

---2. Identify what needs to be found:
Final speed (v)

---3. Write down the First Equation of Motion:
v = u + at

---4. Substitute the known values into the equation:
v = 0 + (2 m/s^2 * 10 s)

---5. Calculate the product of acceleration and time:
v = 0 + 20 m/s

---6. Add the initial speed:
v = 20 m/s

ANSWER: The final speed of the scooter will be 20 m/s.

Why It Matters

Understanding motion is key in many fields! Engineers use it to design safe cars and fast trains. Space scientists at ISRO use it to plan rocket launches and satellite movements. Even in AI/ML, understanding how things move helps in creating self-driving cars and robots.

Common Mistakes

MISTAKE: Confusing initial and final velocity. | CORRECTION: Remember 'u' is initial (starting) velocity and 'v' is final (ending) velocity.

MISTAKE: Forgetting units or using inconsistent units (e.g., km/hr and m/s). | CORRECTION: Always convert all values to the same system of units (like SI units: meters, seconds, m/s, m/s^2) before calculating.

MISTAKE: Not considering 'starts from rest' or 'comes to a stop'. | CORRECTION: If an object 'starts from rest', its initial velocity (u) is 0. If it 'comes to a stop', its final velocity (v) is 0.

Practice Questions

Try It Yourself

QUESTION: A car moving at 10 m/s accelerates at 3 m/s^2 for 5 seconds. What is its final velocity? | ANSWER: 25 m/s

QUESTION: A train traveling at 20 m/s applies brakes and decelerates (negative acceleration) at 4 m/s^2 for 3 seconds. What is its final velocity? | ANSWER: 8 m/s

QUESTION: An auto-rickshaw starts from rest and reaches a speed of 15 m/s in 5 seconds. What is its acceleration? | ANSWER: 3 m/s^2

MCQ

Quick Quiz

Which of the following correctly represents the First Equation of Motion?

v = u + at

v = u - at

s = ut + 1/2 at^2

v^2 = u^2 + 2as

The Correct Answer Is:

The First Equation of Motion relates final velocity (v), initial velocity (u), acceleration (a), and time (t) as v = u + at. Options C and D are other equations of motion.

Real World Connection

In the Real World

When you use a ride-sharing app like Ola or Uber, the app's system uses equations of motion to estimate your arrival time by calculating how the vehicle's speed changes. Traffic engineers also use these equations to design signals and roads, predicting how vehicles accelerate and decelerate to keep traffic flowing smoothly in cities like Mumbai or Delhi.

Key Vocabulary

Key Terms

VELOCITY: Speed in a specific direction. | ACCELERATION: The rate at which velocity changes. | INITIAL VELOCITY: The velocity of an object at the beginning of its motion. | FINAL VELOCITY: The velocity of an object at the end of its motion. | UNIFORM ACCELERATION: When the acceleration remains constant.

What's Next

What to Learn Next

Great job learning about the First Equation of Motion! Next, you should explore the Second and Third Equations of Motion. They will help you understand how distance traveled and squared velocities are related to acceleration and time, completing your understanding of linear motion!