Particle Motion Calculus 3-1

Front

What does it mean for a particle to be at rest?

Back

A particle is at rest when its velocity, v(t), is equal to 0.

Front

How do you determine the total displacement of an object from a motion graph?

Back

Total displacement is the difference between the final and initial positions of the object.

Front

What is the relationship between acceleration and velocity?

Back

The acceleration function is the first derivative of the velocity function.

Front

Given the position function s(t) = -t² - t, how do you find the instantaneous velocity?

Back

Differentiate the position function: v(t) = s'(t) = -2t - 1.

Front

What is the formula for speed when acceleration is zero?

Back

Speed can be found by evaluating the velocity function at the time when acceleration is zero.

Front

Define displacement in the context of particle motion.

Back

Displacement is the change in position of a particle, measured as the straight line distance from the initial to the final position.

Front

What is the significance of the first derivative of the position function?

Back

The first derivative of the position function gives the velocity function, indicating how position changes over time.

Front

How can you find the acceleration of a particle from its position function?

Back

Differentiate the velocity function (the first derivative of position) to find the acceleration function.

Front

What does a velocity of zero indicate about a particle's motion?

Back

A velocity of zero indicates that the particle is momentarily at rest.

Front

How do you calculate the total distance traveled by a particle?

Back

Total distance is calculated by integrating the absolute value of the velocity function over the time interval.