Question

1. explain the difference between a scalar quantity and a vector quantity. provide an example for each

a. scalar:
b. vector quantity:

1. explain the difference between unit and a variable. please provide an example for each.

a. unit:
b. variable:

1. explain the difference between average speed and instantaneous speed.

a. average speed:
b. instantaneous speed:

1. a. if a car is moving at 90 km/hr and it rounds a corner, still going 90 km/hr, does it maintain a constant speed? explain.

b. does it maintain a constant velocity? explain.

Explanation:

1. A scalar quantity has only magnitude. For example, temperature (e.g., 25°C). A vector quantity has both magnitude and direction. For example, velocity (e.g., 50 m/s to the north).
2. A unit is a standard quantity used for measurement, like the meter for length. A variable is a symbol representing an unknown or changing quantity, like \(x\) in an algebraic equation.
3. Average speed is the total distance traveled divided by the total time taken over an interval. Instantaneous speed is the speed at a particular moment in time.
4. a. Yes, it maintains a constant speed because the numerical value of the speed (90 km/hr) does not change.

b. No, it does not maintain a constant velocity. Velocity is a vector, and when the car rounds a corner, its direction changes, even though the speed is the same.

Answer:

1. a. Scalar: Temperature (e.g., 25°C)

b. Vector Quantity: Velocity (e.g., 50 m/s to the north)

1. a. Unit: Meter (for length measurement)

b. Variable: \(x\) in an algebraic - equation

1. a. Average Speed: Total distance divided by total time over an interval.

b. Instantaneous Speed: Speed at a particular moment.

1. a. Yes, because the numerical value of speed doesn't change.

b. No, because direction changes when rounding a corner and velocity is a vector.