Speed, Velocity

11SCI - Mechanics

Finn LeSueur

2020

Ngā Whāinga Ako

  1. Name the metric units of distance, time and speed and give their symbols.
  2. Define the term speed.
  3. 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.
    • e.g 13 meters per second
  • 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?

  1. Knowns
  2. Unknowns
  3. Formula
  4. Substitute
  5. Solve

Question 1: Velocity

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

Mr Le Sueur @ Cattlestop Crag

Question 1: Answer

  1. Knowns: \(\text{distance (d)}=15m\), \(\text{time (t)} = 5.48s\)
  2. Unknowns: \(\text{velocity (v)}\)
  3. Formula: \(v = \frac{\Delta d}{\Delta t}\)
  4. Substitute: \(v = \frac{15}{5.48}\)
  5. 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
CHS Trail Running Club

Question 2: Answer

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

Question 3

Mt Thomas
  • 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

  1. Knowns: \(\text{velocity (v)} = 1.51\frac{m}{s}\), \(\text{time (t)} = 1hr, 18min, 11s = 4691s\)
  2. Unknowns: \(\text{distance (d)}\)
  3. Formula: \(v = \frac{\Delta d}{\Delta t}\)
  4. Substitute: \(1.51 = \frac{d}{4691}\)
  5. 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