Question

The graphs below show the velocity versus time for three different cars: $1,\,2$ and $3$. Rank these cars according to the magnitudes of their velocities, greatest first, at the time indicated on the graph.

A) $1,\,2,\,3$
B) $1,3,\,2$
C) $2,\,1,\,3$
D) $3,\,2,\,1$

Answer 1

Take the graph of the movement of the three different cars. Draw the lines parallel to both the x and y axis. They must touch all the three car’s graphs. Measure the distance of the point of the contact from the velocity axis. Then compare the distances to find the answer.

Complete solution:
From the given graph represents the three cars $1,\,2$ and $3$ . They all possess the different velocity to reach the point of destination. In order to find the highest magnitude of the velocity and the lowest velocity, the straight line is drawn passing through the point $t$ which is perpendicular to the axis of the time and parallel to that of the velocity axis.

This straight line touches all the graphs of the three different cars. Then the straight line which was drawn from the point of contact of the car graph and the line from $t$ touches. It must be perpendicular to the velocity and parallel to the time axis. The point of contact of the two lines with the car graph from the velocity axis is greater for the car $1$ , car $3$ and then for $2$.

Thus the option (B) is correct.

Note: The magnitude of the velocity is greater when the vehicle covers more distance in a very short period of time. In the above graph, if the time is less but the distance covered by the car in the graph is more, then the velocity of the car is greater.