reference q.47179 \try this!\: what relationships in physics obey the following kind of curve called a…

Explanation:

Step1: Recall quadratic - parabolic relationships in physics

One example is the motion of a projectile. When an object is thrown near the Earth's surface with an initial horizontal and vertical velocity, neglecting air - resistance, the vertical displacement (y) of the projectile as a function of the horizontal displacement (x) follows a parabolic path. The equation for the vertical displacement of a projectile launched with initial horizontal velocity (v_{0x}) and initial vertical velocity (v_{0y}) from an initial height (y_0) is (y = y_0+v_{0y}t-\frac{1}{2}gt^{2}), and since (x = v_{0x}t) ((t=\frac{x}{v_{0x}})), substituting (t) into the (y) - equation gives a quadratic relationship between (y) and (x). Also, the displacement of an object in uniformly - accelerated linear motion (s = v_0t+\frac{1}{2}at^{2}) is a quadratic function of time (t) (where (v_0) is the initial velocity and (a) is the acceleration).

Step2: Recall inverse relationships in physics

One well - known example is Boyle's law. For a given mass of an ideal gas at a constant temperature, the pressure (P) and volume (V) of the gas are related by (PV = k) (where (k) is a constant). So, (P=\frac{k}{V}), which is an inverse relationship. As the volume of the gas increases, the pressure decreases, and vice - versa. Another example is the relationship between the current (I) and resistance (R) in a circuit with a constant voltage (V). According to Ohm's law (V = IR), or (I=\frac{V}{R}). When the voltage is held constant, the current and resistance are inversely proportional.

Answer:

Quadratic/parabolic relationships: Projectile motion, uniformly - accelerated linear motion displacement as a function of time. Inverse relationships: Boyle's law (pressure and volume of a gas at constant temperature), current - resistance relationship at constant voltage.