# AP Physics: Displacement, Velocity and Acceleration

Displacement, velocity, and acceleration are three fundamental physics topics. Mastering these will give you a big head start on some of the later, more complex topics! Take a look at these objectives, notes, and practice questions to check your understanding.

### Objective 1

Describe the relationship between displacement, velocity, and acceleration

#### Objective 1 Notes

• Distance and displacement are related, but different
• Both distance and displacement indicate how far an object has moved
• Because distance is a scalar, distance increases whenever an object moves in any direction
• Displacement is a vector: Direction matters!
• A moving object can gain or lose displacement depending on its direction, but a moving object always gains distance
• Displacement’s advantage is that it shows distance between initial and final position, irrespective of the path taken
• Speed and velocity are related, but different °Both terms indicate the rate at which an object is moving
• Recall that a “rate” is any number divided by time
• Speed is distance divided by time; velocity is displacement divided by time
• Because distance is a scalar, speed (distance/time) is also a scalar
• Direction does not matter for speed
• Unlike distance, which always increases or stays the same, speed can increase or decrease over time
• Like distance, speed is never negative
• Because displacement is a vector, velocity is also a vector
• Acceleration is any change in velocity
• An increase or decrease in velocity’s magnitude is acceleration
• Also, a change in velocity’s direction is acceleration!

### Objective 2

Gather information from displacement vs. time graphs

#### Objective 2 Notes

• Imagine an object moving along a straight line path
• A displacement versus time graph shows:
• Either distance or displacement on the y-axis
• Time on the x-axis
• The graph’s slope is crucial!
• If it slopes away from the x-axis, the object moves away from its starting place
• If it slopes toward the x-axis, the object is moving closer to where it started
• If it is flat, then the object is stationary
• Since displacement is related to distance:
• Distance traveled can be calculated from a displacement vs. time graph
• Distance vs. time can be plotted from a displacement vs. time graph
• Slope is always Δy/Δx
• For displacement vs. time, this is Δdisplacement/Δtime = velocity!
• You can calculate an object’s velocity by finding the slope of its displacement vs. time graph
• Where the curve is flat, velocity is zero
• A displacement vs. time graph also gives information about acceleration
• If a segment of the curve is linear, then acceleration is zero
• If a segment of the curve is nonlinear, calculus is required to find acceleration

### Objective 3

Interpret velocity vs. time and acceleration vs. time graphs

#### Objective 3 Notes

• A velocity vs. time graph gives information about velocity, displacement, and acceleration!
• Velocity at a given time can be read directly from the y-axis
• Acceleration is the slope of a velocity vs. time graph
• You cannot tell an object’s displacement from a velocity vs. time graph alone, but you can tell its change in displacement
• To use a velocity vs. time graph to calculate either change in displacement or total distance traveled:
• Find the area between the curve and the x-axis
• For displacement, treat area under negative velocities as “negative area”
• For distance, treat all areas as positive
• An acceleration vs. time graph gives limited information
• The graph gives direct information about acceleration
• You cannot tell velocity directly, though you can find the change in velocity
• To find the change in velocity, find the area between the curve and the x-axis
• You cannot tell displacement from an acceleration vs. time graph, though you can make predictions about how displacement is changing