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Subsection 1.2.2 Exercises

Exercises — Stage 1

1

As they are used in this section, what is the difference between speed and velocity?

2

Speed can never be negative; can it be zero?

3

Suppose you wake up in the morning in your room, then you walk two kilometres to school, walk another two kilometres to lunch, walk four kilometres to a coffee shop to study, then return to your room until the next morning. In the 24 hours from morning to morning, what was your average velocity? (In CLP-1, we are considering functions of one variable. So, at this stage, think of our whole world as being contained in the \(x\)-axis.)

4

Suppose you drop an object, and it falls for a few seconds. Which is larger: its speed at the one second mark, or its average speed from the zero second mark to the one second mark?

5

The position of an object at time \(t\) is given by \(s(t)\text{.}\) Then its average velocity over the time interval \(t=a\) to \(t=b\) is given by \(\dfrac{s(b)-s(a)}{b-a}\text{.}\) Explain why this fraction also gives the slope of the secant line of the curve \(y=s(t)\) from the point \(t=a\) to the point \(t=b\text{.}\)

6

Below is the graph of the position of an object at time \(t\text{.}\) For what periods of time is the object's velocity positive?

Exercises — Stage 2

7

Suppose the position of a body at time \(t\) (measured in seconds) is given by \(s(t)=3t^2+5\text{.}\)

  1. What is the average velocity of the object from 3 seconds to 5 seconds?
  2. What is the velocity of the object at time \(t=1\text{?}\)
8

Suppose the position of a body at time \(t\) (measured in seconds) is given by \(s(t)=\sqrt{t}\text{.}\)

  1. What is the average velocity of the object from \(t=1\) second to \(t=9\) seconds?
  2. What is the velocity of the object at time \(t=1\text{?}\)
  3. What is the velocity of the object at time \(t=9\text{?}\)