# Speed, Velocity

11SCI - Mechanics

Finn LeSueur

2020

## Ngā Whāinga Ako

- Name the metric units of
**distance**, **time** and **speed** and give their symbols.
- Define the term speed.
- Calculate the
**average speed** of objects. Use \(v=d/t\).

## What is Speed?

You know that someone who finishes a race in the shortest time is the fastest. That they have the highest speed.

**Speed is the amount of distance covered in some amount of time**.

## What is Speed?

- Cars display their speed in
*kilometers per hour*
- In Physics we prefer to give speed in the
**number of meters** travelled in **one second**.
- We call this
*meters per second*.

## Calculating Speed

In order to determine speed we need to know two things!

**Distance**: has unit meters (m) and is represented by symbol \(d\) in equations.
**Time**: has unit seconds (s) and is represented by symbol \(t\) in equations.

## Speed vs Velocity

**Speed** is a measure of distance covered in a certain amount of time.
**Velocity** includes a direction
- e.g. 13 meters per second
**east**

## How to Calculate Velocity

\[\begin{aligned}
velocity &= \frac{\text{change in distance}}{\text{change in time}} \\
v &= \frac{\Delta d}{\Delta t} \\
\end{aligned}\]

It is measured in meters per second, also shown as \(\frac{m}{s}\) or \(ms^{-1}\).

## How Do We Solve Problems?

- Knowns
- Unknowns
- Formula
- Substitute
- Solve

## Question 1: Velocity

A rock climber climbs 15 meters in 5.48 seconds. What velocity was he travelling?

## Question 1: Answer

**Knowns:** \(\text{distance (d)}=15m\), \(\text{time (t)} = 5.48s\)
**Unknowns:** \(\text{velocity (v)}\)
**Formula:** \(v = \frac{\Delta d}{\Delta t}\)
**Substitute:** \(v = \frac{15}{5.48}\)
**Solve:** \(v = 2.74\frac{m}{s}\)

## Question 2

- Mr Le Sueur ran 4.61km in 21 minutes and 16 seconds. How fast did he run?
**Hint:** Convert the time and distance to Standard International Units

## Question 2: Answer

**Knowns:** \(\text{distance (d)} = 4.61km = 4610m\), \(\text{time (t)} = 21min, 16s = 1276s\)
**Unknowns:** \(\text{velocity (v)}\)
**Formula:** \(v = \frac{\Delta d}{\Delta t}\)
**Substitute:** \(v = \frac{4610}{1276}\)
**Solve:** \(v = 3.61\frac{m}{s}\)

## Question 3

- Mr Le Sueur ran at \(1.51\frac{m}{s}\) for 1hr, 18min and 11 seconds. How far did he run?
**Hint:** Convert the time to Standard International Units

## Question 3: Answer

**Knowns:** \(\text{velocity (v)} = 1.51\frac{m}{s}\), \(\text{time (t)} = 1hr, 18min, 11s = 4691s\)
**Unknowns:** \(\text{distance (d)}\)
**Formula:** \(v = \frac{\Delta d}{\Delta t}\)
**Substitute:** \(1.51 = \frac{d}{4691}\)
**Solve:** \(1.51 \times 4691 = d = 7083.41m\)

## Mahi Kāinga

Due Monday, August 24th: Mahi Kāinga Booklet Q2, Q3, Q1

## Do Now: sciPAD Page 8, 9, 10