A car accelerated from initial position and then returned at initial point, then

To determine the correct statement about the car's speed and velocity, we can analyze the physics concepts of displacement, distance, velocity, and speed step-by-step:

1. Displacement and Velocity:
Displacement is a vector quantity that represents the shortest straight-line distance from the initial position to the final position of an object.
Since the car starts from an initial position and returns to that same initial point, its final position is identical to its starting position.
Therefore, the net displacement is zero:
$\text{Displacement}=0$

Average velocity is defined as the net displacement divided by the total time elapsed:
$\text{Velocity}=\frac{\text{Displacement}}{\text{Time}}=\frac{0}{t}$
Since the net displacement is zero, the overall velocity is also zero.

2. Distance and Speed:
Distance is a scalar quantity that measures the actual total path length covered by the car during its journey.
Since the car accelerates away and then travels back, it continuously covers physical distance. Unlike displacement, distance is cumulative and cannot be negative or return to zero once accumulated.
Speed is defined as the total distance covered per unit of time:
$\text{Speed}=\frac{\text{Distance}}{\text{Time}}$
Because the total path length (distance) is non-zero and increases as the car moves, the speed increases and remains non-zero.

Thus, the velocity of the car is zero, but its speed increases.