Final answer:
In kinematics, the quantities that will always have the same magnitude pertaining to constant velocity are the rate of change of position with time and the change in position in equal time intervals. An object moving with constant velocity has a consistent rate of change of position, which corresponds to a constant speed over time.
Step-by-step explanation:
The student's question is asking about quantities that relate to the rate of change of position. In other words, it pertains to concepts in kinematics, a branch of Physics that deals with the motion of objects. The pair that will always have the same magnitude are:
- (a) Its rate of change of position with time remains constant.
- (b) Its position changes by the same amount in equal time intervals.
These statements describe an object moving with constant velocity, meaning that its speed and direction do not change. In this case, the rate of change of position is simply the speed, which remains consistent over time. Thus, with a constant rate of change of position, the object covers equal distances in equal time intervals, ensuring that the magnitudes described in (a) and (b) are always the same.
It is important to note that even if the position is different each time, as long as the motion is uniform, the change in position per unit time (velocity) remains constant. Newton's third law is also relevant when considering motion and forces acting on objects in a system, and how these affect movement and interactions between objects. Simplifying kinematic equations, as in the example with the quadratic equation given, often involves canceling out units and solving for unknowns such as time.