Particle Motion Practice

Front

What is the position function of a particle?

Back

The position function s(t) describes the location of a particle at time t. It is often expressed as a function of time, such as s(t) = -t² - t.

Front

How do you find the instantaneous velocity from a position function?

Back

To find the instantaneous velocity, take the derivative of the position function with respect to time. For example, if s(t) = -t² - t, then v(t) = s'(t) = -2t - 1.

Front

What does v(t) > 0 indicate about a particle's motion?

Back

If v(t) > 0, it means the particle is moving to the right.

Front

What does it mean if a particle has negative velocity?

Back

A particle has negative velocity if its position graph is decreasing.

Front

How can you determine when a particle is at rest?

Back

A particle is at rest when its velocity v(t) = 0.

Front

What does a change in direction of a particle's motion indicate?

Back

A change in direction occurs when the velocity of the particle changes sign, which can be found by analyzing the velocity function.

Front

What is the relationship between position, velocity, and acceleration?

Back

Position is the location of a particle, velocity is the rate of change of position, and acceleration is the rate of change of velocity.

Front

What is the formula for average velocity?

Back

Average velocity over an interval [a, b] is given by (s(b) - s(a)) / (b - a).

Front

What does a velocity graph indicate about a particle's motion?

Back

A velocity graph shows how the velocity of a particle changes over time, indicating whether the particle is speeding up, slowing down, or moving in a particular direction.

Front

What is the significance of the derivative in motion analysis?

Back

The derivative of the position function gives the instantaneous velocity, which is crucial for understanding how a particle moves at any given moment.