BC Calculus Straight Line Particle Motion

Front

What is the definition of instantaneous velocity?

Back

Instantaneous velocity is the velocity of a particle at a specific moment in time, calculated as the derivative of the position function with respect to time.

Front

How do you determine when a particle changes direction?

Back

A particle changes direction when its velocity changes sign, which occurs when the derivative of its position function equals zero.

Front

What is the formula for average velocity?

Back

Average velocity is calculated as the change in position divided by the change in time: \( v_{avg} = \frac{s(t_2) - s(t_1)}{t_2 - t_1} \).

Front

If a particle's speed is decreasing, what can be said about its velocity and acceleration?

Back

If a particle's speed is decreasing, its velocity and acceleration have different signs.

Front

What does it mean for a particle's acceleration to be zero?

Back

When a particle's acceleration is zero, it means the particle is moving at a constant velocity.

Front

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

Back

To find the total distance traveled, integrate the absolute value of the velocity function over the given time interval.

Front

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

Back

Position is the integral of velocity, and velocity is the integral of acceleration.

Front

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

Back

The second derivative of the position function represents the acceleration of the particle.

Front

How do you calculate the speed of a particle at a given time?

Back

Speed is the absolute value of velocity, which is the derivative of the position function.

Front

What is the formula for the position of a particle in motion?

Back

The position of a particle can be expressed as a function of time, typically in the form \( s(t) = at^2 + bt + c \), where a, b, and c are constants.