The displacement of a particle moving along an x axis is...

The displacement of a particle moving along an $x$ axis is given by $x=18 t+5.0 t^{2}$, where $x$ is in meters and $t$ is in seconds. Calculate (a) the instantaneous velocity at $t=2.0 \mathrm{~s}$ and (b) the average velocity between $t=2.0 \mathrm{~s}$ and $t=3.0 \mathrm{~s}$.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Displacement (Kinematics)

Displacement in kinematics represents the change in position of a particle. It is often described as a function of time and encapsulates both the direction and magnitude of the particle's movement relative to a reference point.

Instantaneous Velocity

Instantaneous velocity is the rate of change of displacement with respect to time at a specific moment. It is mathematically defined as the derivative of the displacement function with respect to time and provides a precise measure of how fast and in what direction the particle is moving at that exact time.

Average Velocity

Average velocity is defined as the total displacement divided by the total time taken over a given time interval. Unlike instantaneous velocity, it provides a measure of the overall change in position rather than the detailed behavior at each moment.

Differentiation in Kinematics

Differentiation is a mathematical process used in kinematics to compute instantaneous rates of change, such as velocity or acceleration, from a displacement function. By taking the derivative of the displacement with respect to time, one obtains the instantaneous velocity, which is crucial for analyzing the motion of particles.

Transcript

Please give Ace some feedback