5.6.1 Distance and Displacement

• What is the difference between distance and displacement?

  Path length vs change in position
• Scalar quantities have magnitude
• Vector quantities have both magnitude and direction.
• What is the formula for displacement?

  $\text{Final Position} - \text{Initial Position}$
• If an object moves 5 meters north and then 3 meters south, the displacement is 2 meters north.
• Vector quantities include direction while scalar quantities do not.
• Order the common methods to calculate distance from simplest to most accurate:

  1️⃣ Counting steps

  2️⃣ Measuring with tools

  3️⃣ Using formulas
• To calculate distance with constant speed, use the formula $\text{Distance} =$$\text{Speed} \times \text{Time}$, where time is measured in seconds.
• How do you calculate distance if a car travels at 60 km/h for 2 hours?

  120 kilometers
• Match the method to calculate distance with its explanation:

  Counting steps ↔️ Steps multiplied by step length

  Measuring tools ↔️ Use rulers or odometers

  Formulas ↔️ Calculate using speed and time
• Vector addition can be used to calculate displacement by adding the components of displacement vectors.
• If an object moves 3 meters north and 4 meters east, the displacement is 5 meters.
• How do you calculate displacement using coordinates?

  Final position - initial position
• Match the method to calculate displacement with its example:

  Vector addition ↔️ 3m North, 4m East, displacement = 5m

  Coordinates ↔️ From (1, 2) to (4, 6), displacement = (3, 4)
• The overall displacement magnitude is calculated using the Pythagorean theorem.
• What is the overall displacement magnitude if an object moves from (1, 2) to (4, 6)?

  5 meters
• The overall displacement magnitude is the same as the distance traveled.

  False
• Vector addition uses the Pythagorean theorem to find the overall displacement from two perpendicular vectors.
• What type of quantity is distance?

  Scalar
• Displacement includes both magnitude and direction.
• An object moves 5m east and 2m west. The displacement is 3 meters east.
• What are two examples of scalar quantities?

  Distance and speed
• Match the scalar quantity with its corresponding vector quantity:

  Distance ↔️ Displacement

  Speed ↔️ Velocity

  Mass ↔️ Force

  Time ↔️ Acceleration
• What is the formula for calculating distance using speed and time?

  $Distance =$$Speed \times Time$
• A person walks 15 steps, each 1 meter long. The distance traveled is 15 meters.
• Measuring tools like rulers and odometers are used for precise distance measurements.
• What does the gradient of a distance-time graph represent?

  Speed
• A steeper gradient on a distance-time graph indicates a higher speed of the object.
• A straight line with a positive slope on a distance-time graph shows constant speed.
• Match the slope of a displacement-time graph with its meaning:

  Positive slope ↔️ Moving away from starting point

  Negative slope ↔️ Moving back towards starting point

  Zero slope ↔️ Stationary
• What does a curved line on a displacement-time graph indicate?

  Variable velocity
• A car moving at a constant velocity of 20 m/s for 5 seconds has a displacement of 100 meters.
• Displacement is always shorter than distance if an object changes direction.