Final answer:
Instantaneous velocity is a vector quantity providing the speed and direction of an object at a specific time, while instantaneous speed is the magnitude of this velocity, showing how fast the object is moving without direction.
Step-by-step explanation:
Understanding Instantaneous Velocity and Speed
At a certain time instant, the vector quantity we're discussing is instantaneous velocity, which represents both the speed and direction of an object at that exact moment. The instantaneous speed at this same instant is the magnitude of the instantaneous velocity, reflecting how fast the object is moving without regard to its direction. Therefore, if the instantaneous velocity of a particle at t = 0.25 s, t = 0.50 s, and t = 1.0 s were given, we could determine the particle's speed at these times simply by calculating the magnitude of its velocity vector.
Since instantaneous speed is a scalar quantity, it does not provide any information about the direction of motion. To understand the motion of the particle thoroughly, both the scalar instantaneous speed and the vector instantaneous velocity need to be considered. Kinematics studies these properties to describe motion.