### Subsection1.2.2Exercises

###### 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?

###### 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 $t=9\text{?}$