Question

The $x-t$ graph for motion of a car is given below.

With reference to the graph, which of the given option(s) is/are incorrect?

• A. The instantaneous speed during the interval $t=5 \,s$ to $t=10 \,s$ is negative at all time instants during the interval.
• B. The velocity and the average velocity for the interval $t=0\, s$ to $t=5 \,s$ are equal and positive.
• C. The car changes its direction of motion at $t=5 \,s$.
• D. The instantaneous speed and the instantaneous velocity are positive at all time instants during the interval $t=0\, s$ to $t=5 \,s$.

Answer 1

Answer: (A)

The instantaneous speed is always positive as it is the magnitude of the velocity at an instant. So, it is positive during $t=5\, s$ to $t=10\, s$.
For $t=0\, s$ to $t=5\, s$, the motion is uniform and $x-t$ graph has positive slope. So, the velocity and average velocity, instantaneous velocity and instantaneous speed are equal and positive.
During $t=0\, s$ to $t=5\, s$, the slope of the graph is positive, hence the average velocity and the velocity both are positive.
During $t=5 \, s$ to $t=10\, s$, the slope of the graph is negative, hence the velocity is negative. Since, there is a change in sign of velocity at $t=5\, s$, so the car changes its direction at this instant.
Hence, option (a) is incorrect, while all other are correct.