Particle Motion for a Graph: Calculus

Speed of the particle is increasing given position

The graph is:

• increasing and concave up

• decreasing and concave down

Particle at rest given position

horizontal tangent line

Speed of the particle is decreasing given postition

The graph is:

• increasing and concave down

• decreasing and concave up

Particle is moving to the right given position

slope of the graph is increasing

Particle is moving to the left given position

slope of the graph is decreasing

Particle has a positive acceleration given position

graph is concave up

Particle has a negative acceleration given position

graph is concave down

Particle is moving to the right given velocity

graph is positive (above the x-axis)

Particle is moving to the left given velocity

graph is negative (below the x-axis)

Particle has a negative acceleration given velocity

slope of the graph is decreasing

Particle has a positive acceleration given velocity

slope of the graph is increasing

Particle is at rest given velocity

x-intercepts of the graph (touching or crossing the x-axis)

The speed of the particle is decreasing given velocity

The graph is:

• positive and decreasing

• negative and increasing

The speed of the particle is increasing given velocity

The graph is:

• positive and increasing

• negative and decreasing