What is Displacement?

S6-SA3-0004

Grade Level:

Class 10

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

Definition

What is it?

Displacement is the shortest distance between an object's starting point and its ending point, along with the direction. It tells us how far an object is from its initial position, regardless of the path taken.

Simple Example

Quick Example

Imagine you walk from your home to the neighbourhood chai shop, which is 50 meters east. Then you walk 50 meters west back to your home. Your total distance covered is 100 meters, but your displacement is 0 meters because you ended up at your starting point (home).

Worked Example

Step-by-Step

QUESTION: A delivery rider starts from a shop, rides 4 km North, then turns and rides 3 km East. What is the magnitude of the rider's displacement from the shop?

1. Identify the starting point and ending point. Starting point is the shop. Ending point is after riding 4 km North and 3 km East.
---2. Visualize the path. The rider forms a right-angled triangle with the shop, the point after going North, and the final point after going East.
---3. The North journey is one side (4 km), and the East journey is the other side (3 km) of a right-angled triangle. The displacement is the hypotenuse.
---4. Use the Pythagorean theorem: Displacement^2 = (North distance)^2 + (East distance)^2
---5. Displacement^2 = (4 km)^2 + (3 km)^2
---6. Displacement^2 = 16 km^2 + 9 km^2
---7. Displacement^2 = 25 km^2
---8. Displacement = sqrt(25 km^2) = 5 km.
ANSWER: The magnitude of the rider's displacement is 5 km.

Why It Matters

Understanding displacement is crucial for engineers designing bridges or tracking satellites in space, ensuring they reach the correct destination. It's also vital in medicine for tracking the movement of cells or medical devices inside the body, helping doctors diagnose and treat illnesses effectively.

Common Mistakes

MISTAKE: Confusing displacement with distance. | CORRECTION: Remember, distance is the total path covered, while displacement is the shortest straight-line path from start to end, including direction.

MISTAKE: Forgetting that displacement has a direction. | CORRECTION: Always mention the direction (e.g., 5 km North-East) when stating displacement. If only magnitude is asked, then direction isn't needed.

MISTAKE: Assuming displacement is always positive. | CORRECTION: Displacement can be zero (if you return to the start) or negative (if you move in the opposite direction from your defined positive direction).

Practice Questions

Try It Yourself

QUESTION: A student walks 100 meters from their home to a bus stop. What is their displacement? | ANSWER: 100 meters from home to bus stop (in the direction they walked).

QUESTION: An auto-rickshaw travels 6 km East, then 8 km South. What is the magnitude of its displacement from the starting point? | ANSWER: 10 km.

QUESTION: A cricket ball is hit 30 meters towards the boundary. A fielder runs 10 meters towards the ball from his position. What is the displacement of the ball relative to its initial position when the fielder catches it, assuming the fielder was directly in the path? | ANSWER: 30 meters towards the boundary.

MCQ

Quick Quiz

Which of the following is true about displacement?

It is always equal to the distance covered.

It is a scalar quantity.

It has both magnitude and direction.

It can never be zero.

The Correct Answer Is:

Displacement is a vector quantity, meaning it has both magnitude (how much) and direction (where). It is not always equal to distance and can be zero.

Real World Connection

In the Real World

ISRO scientists use displacement calculations to track the precise position of satellites orbiting Earth, ensuring they stay on course. Similarly, GPS in your mobile phone uses displacement principles to show you the shortest route from your current location to your destination, like finding the quickest way to your favourite biryani shop.

Key Vocabulary

Key Terms

MAGNITUDE: The size or numerical value of a quantity | DIRECTION: The path along which something moves or lies | VECTOR QUANTITY: A quantity that has both magnitude and direction | SCALAR QUANTITY: A quantity that only has magnitude | INITIAL POSITION: The starting point of an object

What's Next

What to Learn Next

Now that you understand displacement, you're ready to learn about 'Velocity'. Velocity builds on displacement by adding the concept of time, telling us how fast an object's displacement changes. Keep up the great work!