Particle Motion (Calculus)

Speed is determined by the absolute value of velocity, |v(t)|.

Speed is determined by the average distance traveled over time.

Speed is determined by the change in position divided by time.

Speed is determined by the maximum velocity reached during motion.

The particle is moving to the left.

The particle is moving to the right.

The particle is at rest.

The particle is accelerating forward.

Velocity

Acceleration

Displacement

Force

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

The velocity function is the second derivative of the position function.

The velocity function is the integral of the position function.

The velocity function is the average rate of change of the position function.

It indicates that the particle is slowing down.

It indicates that the particle is speeding up.

It indicates that the particle is moving in the opposite direction.

It indicates that the particle is at rest.

(s(b) - s(a)) / (b - a)

(s(a) + s(b)) / 2

(b - a) / (s(b) - s(a))

s(b) - s(a)

The slope of a velocity-time graph represents speed, while the area under the curve represents distance.

The slope of a velocity-time graph represents acceleration, while the area under the curve represents displacement.

The slope of a velocity-time graph represents velocity, while the area under the curve represents time.

The slope of a velocity-time graph represents force, while the area under the curve represents energy.

Instantaneous velocity is the velocity at a specific moment in time, while average velocity is calculated over an interval.

Instantaneous velocity is the total distance traveled divided by the total time, while average velocity is the speed at a specific moment.

Instantaneous velocity is always greater than average velocity, as it accounts for acceleration.

Instantaneous velocity is the velocity of an object in free fall, while average velocity is the velocity of an object in uniform motion.

It determines the maximum height of the particle's motion.

It is the velocity of the particle at time t=0, which is crucial for solving motion problems.

It affects the acceleration of the particle throughout its motion.

It is irrelevant to the overall motion of the particle.

The particle is at rest.

The particle is moving at a constant velocity.

The particle is speeding up.

The particle is slowing down.