Linear relations

Exercise 1

Here you see the graphs of four linear functions in one coordinate system.

Give the function rule for each of the graphs.

Exercise 2

Give the equation of a straight line $l$ that is given by:

a

$l$ goes through points $(30, 68)$ and $(34, 56)$ .

b

$l$ goes through points $(-2, 100)$ and $(-3, 100)$ .

c

$l$ has gradient $0.5$ and goes through $(-2, 4)$ .

d

$l$ is the $x$ -axis.

e

$l$ is the $y$ -axis.

Exercise 3

Algebraically determine the coordinates of the point of intersection of lines $l$ passing through $P (13, 8)$ and $Q (43, 48)$ and $m$ passing through $R (43, 28)$ en $T (23, 38)$ .

Exercise 4

Gases behave according to the law of Gay-Lussac. The volume $V$ (in m³) of an amount of gas under a given pressure is dependent on temperature $T$ (in °C). The following formula describes this dependence:
$\frac{V (T)}{T + 273} = \frac{V (0)}{273}$
where $-273$ °C is absolute zero and $V (0)$ is the volume at $0$ °C.

a

Reorganize this formula to give: $V (T) = V (0) \cdot (1 + \frac{1}{273} T)$ .

b

Explain why you can use a linear model here. What assumption is necessary for the model to be valid? Which domain do you have to choose?

c

Assume $V (0) = 1$ m³ and show the corresponding graph on your calculator. Write down the window settings that you used.

d

What is the volume of this gas at room temperature?

e

At what temperature has the volume increased by a factor of $1.5$ ?

Exercise 5

An object in uniform motion moves at a constant speed in a straight line. In physics, such a motion is described by the formula:
$s (t) = s (0) + v \cdot t$
where $s (t)$ is the distance covered (in m) after $t$ seconds.

a

What does $s (0)$ represent? And what is $v$ ?

b

Assume that for a given object $s (0) = 0$ and $v = 20$ m/s. Use your calculator to plot the corresponding graph of $s (t)$ .

c

A second object is $400$ m up ahead and moves along the same trajectory with a speed of $15$ m/s. Write down the formula that describes to the motion of this second object and plot the corresponding graph.

d

Calculate how long it will take the first object to catch up with the second object.

Exercise 6

An object in uniformly accelerated motion moves in a straight line with constant acceleration $a$ (in m/s²). In physics such a motion is described by the formula:
$v (t) = v (0) + a \cdot t$
where $v (t)$ is the speed (in m/s) after $t$ seconds.

a

What does $v (0)$ represent?

b

An object has an initial speed of $40$ m/s. The constant acceleration is about $10$ m/s². How long (in seconds) does it take until the object has reached a speed of $350$ m/s?

c

An object with a mass $m$ of $1000$ kg is moving at a constant speed of $40$ m/s. In order to bring this object to a standstill, a certain braking force $F$ (in Newton) has to be applied. The object has to stop moving within $8$ seconds. You know that $F = m \cdot a$ with $F$ in Newton, $m$ in kg and acceleration $a$ in m/s². Calculate the required braking force $F$ .

Exercises