The $x$ - $t$ graph for motion of a car is given below. With reference to the graph which of the giv

Question

The $x$ - $t$ graph for motion of a car is given below. With reference to the graph which of the given statement(s) is/are correct? \ I. The instantaneous speed during the interval $t=5 \mathrm{~s}$ to $t=10 \mathrm{~s}$ is negative at all time instants during the interval. \ II. The velocity and the average velocity for the interval $t=0 \mathrm{~s}$ to $t=5 \mathrm{~s}$ are equal and positive. \ III. The car changes its direction of motion at $t=5 \mathrm{~s}$.\  IV. The instantaneous speed and the instantaneous velocity is positive at all time instants during the interval $t=0 \mathrm{~s}$ to $t=5 \mathrm{~s}$. Choose the correct option :

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(d) : I. The instantaneous speed is always positive as it is the magnitude of the velocity at an instant. II. For $t=0 \mathrm{~s}$ to $t=5 \mathrm{~s}$, the motion is uniform. So, the average velocity and the instantaneous velocity are equal. III. During $t=0 \mathrm{~s}$ to $t=5 \mathrm{~s}$, the slope of the graph is positive, hence, the average velocity and the velocity both are positive. During $t=5 \mathrm{~s}$ to $t=10 \mathrm{~s}$, the slope of the graph is negative, hence, the velocity is negative. Since, there is change in sign of velocity at $t=5 \mathrm{~s}$, the car changes its direction at that instant. IV. In figure, instantaneous velocity during $t=0 \mathrm{~s}$ to $t=5 \mathrm{~s}$ is positive Also, the speed is always a positive value.