Here you see the graphs of four linear functions in one coordinate system.
Give the function rule for each of the graphs.
Give the equation of a straight line that is given by:
goes through points and .
goes through points and .
has gradient and goes through .
is the -axis.
is the -axis.
Algebraically determine the coordinates of the point of intersection of lines passing through and and passing through en .
Gases behave according to the law of Gay-Lussac. The volume (in m3) of an amount of gas under a given pressure is dependent on temperature (in °C). The following formula describes this dependence:
where °C is absolute zero and is the volume at °C.
Reorganize this formula to give: .
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?
Assume m3 and show the corresponding graph on your calculator. Write down the window settings that you used.
What is the volume of this gas at room temperature?
At what temperature has the volume increased by a factor of ?
An object in uniform motion moves at a constant speed in a straight line. In physics,
such a motion is described by the formula:
where is the distance covered (in m) after seconds.
What does represent? And what is ?
Assume that for a given object and m/s. Use your calculator to plot the corresponding graph of .
A second object is m up ahead and moves along the same trajectory with a speed of m/s. Write down the formula that describes to the motion of this second object and plot the corresponding graph.
Calculate how long it will take the first object to catch up with the second object.
An object in uniformly accelerated motion moves in a straight line with constant acceleration
(in m/s2). In physics such a motion is described by the formula:
where is the speed (in m/s) after seconds.
What does represent?
An object has an initial speed of m/s. The constant acceleration is about m/s2. How long (in seconds) does it take until the object has reached a speed of m/s?
An object with a mass of kg is moving at a constant speed of m/s. In order to bring this object to a standstill, a certain braking force (in Newton) has to be applied. The object has to stop moving within seconds. You know that with in Newton, in kg and acceleration in m/s2. Calculate the required braking force .