Acceleration

Definition

Acceleration is the rate of change of velocity with respect to time. It is a vector quantity, meaning it has both magnitude and direction.

5 Must Know Facts For Your Next Test

1. Mathematically, acceleration is the second derivative of position with respect to time: $a(t) = \frac{d^2x}{dt^2}$.
2. Acceleration can be positive (speeding up) or negative (slowing down), often referred to as deceleration.
3. In calculus, you may need to find acceleration by differentiating the velocity function: $a(t) = v'(t)$.
4. If given a position function $x(t)$, you can find acceleration by differentiating twice: $a(t) = x''(t)$.
5. Units for acceleration are typically meters per second squared ($m/s^2$).

Review Questions

• How do you mathematically define acceleration in terms of derivatives?
• What is the relationship between velocity and acceleration?
• If you have a position function $x(t)$, how do you determine the acceleration?

Related terms

Velocity: The rate of change of position with respect to time; first derivative of position.

Position Function: $x(t)$ represents an object's location as a function of time.

Second Derivative: $\frac{d^2y}{dx^2}$ represents the rate at which the first derivative changes; used to find acceleration from position functions.