Question

The graph shows a journey in a car. Which of the statements most likely describes the journey back to the starting point at the the portion of the graph labeled O?

Answer 1

The car travels different distance per unit of time.

Explanation:

Distance per unit time on graph will be = Distance for a given point time/ Time

if we see this in terms of x and y , it will be the slope of the curve on given graph.

y/x = slope of graph

Now solving it becomes easier.

We know that

slope =
`tan\alpha` where
`\alpha` is the positive angle with x axis

For part I

The slope will be tan of some acute angle and we know that

tan of acute angle varies between 0 to 1.

Distance per unit time on graph will be between 0 to 1

for part J

Line is parallel to x axis and hence angle with x axis will be 0

thus,

tan 0 = 0

slope of part j is 0

Distance per unit time on graph will be = 0

For part k the distance is changing at each point hence we have to find

distance for each point and time for each point on coordinate and hence

Distance per unit time on graph for part k will be different at each point.

part L and N can be explained on similar grounds as J

O can be explained by explanation for part K.

Part M can be explained by explanation of part I

here difference will be that slope is obtuse and hence

slope or distance per unit time will be negative

as tan for obtuse angle is between -1 to 0.

Thus, correct option will be

The car travels different distance per unit of time.