Final answer:
In physics, velocity, which is a vector quantity, can be zero at the peak of a projectile's path or when an object changes direction. For projectile motion on level ground, when there's no air resistance, the vertical velocity is zero at the peak of its flight, although horizontal velocity remains constant. The slope of the position function is zero when instantaneous velocity is zero.
Step-by-step explanation:
The question of whether there can be an instant when velocity is zero is a common one in physics, especially when discussing motion. For an object in motion, there are indeed instances where the velocity can be zero. This typically happens at the peak of a projectile's path when it momentarily stops ascending and before it starts descending, or when an object changes direction. The velocity is a vector quantity, meaning it has both magnitude and direction so, if the displacement doesn't change over a time period, the average velocity can be zero.
For projectile motion on level ground with negligible air resistance, assuming the initial angle is neither 0° nor 90°, the velocity of the projectile is zero at the peak of its trajectory in the vertical component, but not in the horizontal component. The horizontal velocity remains constant due to the absence of air resistance and no horizontal forces acting (neglecting air resistance). The vertical component of velocity reaches zero at the peak height.
It's important to differentiate between speed and velocity. Speed is a scalar quantity and refers only to how fast an object is moving, while velocity includes direction. Thus, instantaneous speed and velocity can indeed be the same if there is no change in the direction of motion.
Lastly, looking at the slope of the position function, if the instantaneous velocity is zero, the slope of the position vs. time graph at that instant would also be zero, which graphically represents that there is no change in position over that instant in time.