The graph of an object's motion (along the $x-$ axis) is shown in the figure. The instantaneous velocity of the object at points $A$ and $B$ are $v_A$ and $v_B$ respectively. Then

Given below are two statements:
Statement $I:$ Area under velocity-time graph gives the displacement of the body in a given time.
Statement $II:$ Area under acceleration-time graph is equal to the change in velocity in the given time.
In the light of given statements, choose the correct answer from the options given below.

What does a vehicle's speedometer measure: instantaneous velocity or instantaneous speed?

The position-time graph of a particle moving along a straight line is shown,which is in the form of a semicircle starting from $t=2 \, s$ to $t=8 \, s$. Select the correct statement.

Which one of the following graphs for a body moving along a straight line is possible?

The displacement $x$ of a particle varies with time $t$ as $x = a e^{-\alpha t} + b e^{\beta t}$,where $a, b, \alpha, \text{and } \beta$ are positive constants. The velocity of the particle will: