The reason an object on the equator has its maximum velocity at noon and minimum velocity at midnight is due to the combination of two factors: the rotation of the Earth on its axis and the orbit of the Earth around the Sun.
Rotation of the Earth: The Earth rotates on its axis, completing one full rotation approximately every 24 hours. This rotation causes objects on the Earth's surface to move in a circular path around the Earth's axis. At the equator, the distance traveled in one full rotation is the largest compared to other latitudes. Since the time taken to complete one rotation is fixed, the linear velocity of an object on the equator is highest when it is at the furthest distance from the Earth's axis, which occurs at noon and midnight.
Orbit of the Earth around the Sun: The Earth follows an elliptical orbit around the Sun. This means that the Earth is not always at the same distance from the Sun throughout the year. However, the effect of the Earth's orbit on the velocity of an object on the equator is relatively minor compared to the rotation of the Earth. Therefore, the primary reason for the variation in velocity is the rotation of the Earth.
To summarize, an object on the equator has its maximum velocity at noon and minimum velocity at midnight due to the combination of the Earth's rotation on its axis and the resulting circular motion of objects on its surface. The effect of the Earth's orbit around the Sun is relatively minimal in this context.