Question: A car's position in relation to time is plotted on the graph. What can be said about the car during segment B?
A) The car travels for 80 seconds during segment B.
B) The car has come to a stop and has zero velocity.
C) The car is traveling faster during segment B than in segment C.
D) The car is traveling with a constant velocity due to the flat line of the graph.
The correct answer is "the car has come to a stop and has zero velocity."
Explanation:
According to the theory of graphs, ‘the straight line parallel to x axis’ means the quantity given on y axis is not changing or is constant with respect to the change in the quantity on x axis. This is why because the slope of that particular straight line is zero.
Mathematically, the slope is defined as the tangent (trigonometry) of the angle made by the segment with the x axis or it is also defined as the ratio of change in the quantity on y-axis to change in the quantity on x-axis.
[tex]Slope = Tan \theta[/tex]
Here, is the angle made by the segment of graph with x-axis
The slope can also be expressed as:
[tex]Slope = \frac{Change in quantity given on y -axis}{change in quantity in x- axis}[/tex]
Here, the quantity given on y axis is car’s position and that given on x axis is time taken by the car to travel.
The slope of position-time graph gives velocity. So, by the definition of slope, we have
[tex]Velocity = \frac{change in position}{change in time}[/tex]
Here, as shown in the graph, the two ends of the segment B have same values of position on y axis. So, change in position will be zero.
Substitute for in above expression.
[tex]Velocity = 0 m/s[/tex]
This shows that the speed of the car in the segment B of the graph will be zero as there is no change in the position of the car with respect to time.
Thus, option (B) is correct .i.e. the car has come to a stop and has zero velocity.
