# Vectors and Kinematics (Part 1 of 2)

You can find the second part of this series here: Vectors and Kinematics (Part 2 of 2).

## Vectors and Scalars

- A vector is a quantity that has magnitude (size) and direction. For example:
- Velocity, displacement, acceleration

- A scalar is a quantity that has only magnitude (size). For example:
- Speed, distances, temperatures, mass

5 miles per hour = scalar quantity

5 miles per hour, east = vector quantity

## Displacement

Displacement is the change in position of an object. This is **not** the total distance an object has travelled.

The total distance travelled can be greater than the magnitude of its displacement.

- A’s Displacement = Δx = x
^{finish}– x^{start}= e.g. 10 meters - Distance = total length of distance travelled, for the sake of the example, 20 meters

### Velocity

Velocity is a vector quantity. It is speed, **and direction**. Instantaneous velocity is the speed and direction at a certain point in time.

### Acceleration

Acceleration is the change in velocity over time. It is also a vector quantity.

For example: 0 – 60 miles per hour, in 3 seconds east

- a = Δv / Δt
- 60 – 0 (east) / 3 seconds = 20 miles per hour/seconds (east)

## Linear Motion

Linear motion = change in distance / change in time.

**Question:** A ball thrown straight up in the air at 20 meters / second

- How long will the ball move up?
- How high will the ball travel?

Gravity = 9.8 meters / second

^{2 }⇒ velocity due to gravity = g × tDistance = v × t

Distance due to gravity = ½ g t

^{2}

**Answer Part 1:**

Initial velocity = 20 m/s

∴ 20 m/s = 10 m/s^{2} t * ← gravity approximation (9.8 to 10)*

∴ t = 2 seconds

**Part 2:**

20 m/s × 2 – ½ (10 m/s^{2})(2)^{2}

40 m – 20 m

= 20 meters, before it starts to descend