One-Dimensional Constant-Acceleration Kinematics and Pursuit

All flashcards

What does the subscript 0 mean in kinematics?

It identifies an initial value, such as initial position $x_0$ or initial velocity $v_0$.

How is displacement defined?

Displacement is the change in position: $\Delta x = x - x_0$. It includes direction and is not necessarily the total path length.

What does constant acceleration mean?

Acceleration has the same value throughout the interval, so velocity changes by equal amounts during equal time intervals.

What does a negative acceleration tell you?

It points in the negative coordinate direction. Whether it speeds an object up or slows it down depends on the object's velocity direction.

What is average velocity?

The displacement divided by the elapsed time: $v_{avg}=\Delta x/\Delta t$.

Quiz questions

1. Which equation relates velocity and displacement for motion with constant acceleration when elapsed time is not needed?Answer: $v^2=v_0^2+2a(x-x_0)$
2. Which equation gives position after a known time for motion with constant acceleration?Answer: $x=x_0+v_0t+\frac{1}{2}at^2$
3. A motion event has an interval of changing acceleration. How can it often be analyzed using constant-acceleration models?Answer: Divide it into stages and model each stage separately.
4. Why is reaction distance added to braking distance when calculating total stopping displacement?Answer: The vehicle travels during the reaction interval before braking begins.
5. At the catch-up instant in a pursuit problem, what condition must the two objects satisfy?Answer: They have the same position at the same elapsed time.