$v = v_0 + at$

Definition

$v = v_0 + at$ is an equation that represents the relationship between an object's velocity, initial velocity, acceleration, and time. It describes how an object's velocity changes over time when it is experiencing a constant acceleration.

5 Must Know Facts For Your Next Test

1. The equation $v = v_0 + at$ is used to calculate an object's velocity at any given time when the object is undergoing constant acceleration.
2. The variable $v$ represents the object's final velocity, $v_0$ represents the object's initial velocity, $a$ represents the object's constant acceleration, and $t$ represents the time elapsed.
3. This equation can be used to describe both linear and rotational motion, as long as the acceleration is constant.
4. The equation is derived from the definition of acceleration as the rate of change of velocity with respect to time.
5. Rearranging the equation can also yield other useful relationships, such as $a = (v - v_0)/t$ and $t = (v - v_0)/a$.

Review Questions

• Explain how the equation $v = v_0 + at$ can be used to describe the motion of an object experiencing constant acceleration.
  • The equation $v = v_0 + at$ describes the relationship between an object's final velocity ($v$), initial velocity ($v_0$), acceleration ($a$), and the time elapsed ($t$). If the acceleration of an object is constant, this equation can be used to calculate the object's velocity at any point in time. For example, if an object starts with an initial velocity of $v_0$ and experiences a constant acceleration of $a$, then its velocity at time $t$ can be determined using this equation. This equation is fundamental for analyzing the motion of objects under the influence of a constant force or acceleration.
• Describe how the variables in the equation $v = v_0 + at$ can be rearranged to solve for other quantities of interest.
  • The equation $v = v_0 + at$ can be rearranged to solve for other variables of interest. For instance, if you know the object's initial velocity ($v_0$), acceleration ($a$), and final velocity ($v$), you can rearrange the equation to solve for the time ($t$) using the formula $t = (v - v_0)/a$. Similarly, if you know the object's initial velocity ($v_0$), final velocity ($v$), and time ($t$), you can rearrange the equation to solve for the acceleration ($a$) using the formula $a = (v - v_0)/t$. This flexibility in rearranging the equation allows you to use it to solve a variety of problems involving constant acceleration motion.
• Explain how the equation $v = v_0 + at$ can be used to analyze the motion of an object in both linear and rotational contexts.
  • The equation $v = v_0 + at$ can be applied to describe the motion of an object in both linear and rotational contexts, as long as the acceleration is constant. In the case of linear motion, the variables $v$, $v_0$, $a$, and $t$ would represent the object's linear velocity, initial linear velocity, linear acceleration, and time, respectively. In the case of rotational motion, these variables would represent the object's angular velocity, initial angular velocity, angular acceleration, and time. The fundamental relationship between an object's final velocity, initial velocity, acceleration, and time is captured by this equation, regardless of whether the motion is linear or rotational in nature.

Related terms

Velocity: Velocity is the rate of change of an object's position with respect to time, and is a vector quantity with both magnitude and direction.

Acceleration: Acceleration is the rate of change of an object's velocity with respect to time, and is also a vector quantity.

Initial Velocity: The initial velocity, $v_0$, is the velocity of an object at the starting time of a motion.