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How do you find instantaneous velocity from a position vs. time graph?
Determine the slope of the tangent line at the point of interest on the position vs. time graph.
How do you find displacement from a velocity vs. time graph?
Calculate the area under the curve between the initial and final times on the velocity vs. time graph.
How do you find the change in velocity from an acceleration vs. time graph?
Calculate the area under the curve between the initial and final times on the acceleration vs. time graph.
How do you solve for final velocity with constant acceleration, given initial velocity and time?
Use the equation: $v_{x}=v_{x 0}+a_{x} t$.
How do you solve for final position with constant acceleration, given initial position, initial velocity, and time?
Use the equation: $x=x_{0}+v_{x 0} t+\frac{1}{2} a_{x} t^{2}$.
What is the effect of a positive slope on a position vs. time graph?
The object is moving in the positive direction.
What is the effect of a negative slope on a velocity vs. time graph?
The object is slowing down (decelerating).
What is the effect of gravity on an object thrown upwards near Earth's surface?
The object experiences a constant downward acceleration of approximately 10 m/s².
What happens to the maximum height of a projectile if gravity is halved?
The maximum height doubles.
What is the effect of constant acceleration on an object's velocity?
The object's velocity changes uniformly over time.
Define instantaneous velocity.
The rate of change of position with respect to time at a specific instant; mathematically, $v_{x}=\frac{d x}{d t}$.
Define instantaneous acceleration.
The rate of change of velocity with respect to time at a specific instant; mathematically, $a_{x}=\frac{d v_{x}}{d t}$.
What is displacement?
The change in position of an object. On a velocity vs. time graph, it's the area under the curve: $\Delta x=\int_{t_{1}}^{t_{2}} v_{x}(t) d t$.
Define gravitational acceleration (g).
The constant downward acceleration experienced by objects near Earth's surface due to gravity, approximately $g \approx 10 \mathrm{~m} / mathrm{s}^{2}$.
What are kinematic equations?
Equations that describe the motion of objects with constant acceleration, relating position, velocity, time, and acceleration.