One-Dimensional Constant-Acceleration Kinematics: Equations and Problem Solving

All flashcards

What does the subscript $0$ indicate in kinematics?

It marks 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 is not necessarily total distance traveled.

How is average velocity calculated under constant acceleration?

It is the arithmetic mean of initial and final velocity: $\bar{v}=\frac{v_0+v}{2}$.

What equation gives final position from average velocity?

$x=x_0+\bar{v}t$.

When is the time-independent velocity equation useful?

When time is not given or needed: $v^2=v_0^2+2a(x-x_0)$.

Quiz questions

1. An object moves in the negative direction, and its acceleration is also negative. Assuming the acceleration continues, what happens to its speed?Answer: Its speed increases.
2. Which equation relates final velocity, initial velocity, acceleration, and displacement without using time?Answer: $v^2=v_0^2+2a(x-x_0)$
3. For the same braking deceleration, how does stopping distance change if initial speed doubles?Answer: It becomes four times as large.
4. A vehicle travels $12\ \text{m}$ during reaction time and then travels $48\ \text{m}$ while braking. What is its total stopping distance?Answer: $60\ \text{m}$
5. A car's modeled travel time is measured from $t=0$. A quadratic calculation gives roots of $8\ \text{s}$ and $-12\ \text{s}$. Which root represents the travel time after the motion begins?Answer: $8\ \text{s}$