Displacement Calculator
Calculate displacement using velocity, acceleration, or kinematics equations
Calculate Displacement
Duration of motion
Constant velocity throughout motion
Displacement Results
Calculation Details
Example Calculations
Constant Velocity
Problem: A car travels at 60 km/h for 2 hours
Given: v = 60 km/h, t = 2 h
Formula: d = v × t
Solution: d = 60 × 2 = 120 km
Constant Acceleration
Problem: Object starts at rest, accelerates at 2 m/s² for 5 s
Given: v₀ = 0 m/s, a = 2 m/s², t = 5 s
Formula: d = v₀t + ½at²
Solution: d = 0 + ½(2)(25) = 25 m
Initial & Final Velocities
Problem: Object accelerates from 10 m/s to 30 m/s in 4 s
Given: v₀ = 10 m/s, vf = 30 m/s, t = 4 s
Formula: d = (v₀ + vf)/2 × t
Solution: d = (10 + 30)/2 × 4 = 80 m
Real-world: Free Fall
Problem: Object dropped from rest for 3 seconds
Given: v₀ = 0 m/s, a = 9.81 m/s², t = 3 s
Formula: d = v₀t + ½at²
Solution: d = 0 + ½(9.81)(9) = 44.1 m
Key Concepts
Displacement vs Distance
Displacement is the straight-line distance between start and end points, while distance is the total path traveled.
Vector Quantity
Displacement has both magnitude and direction, making it a vector quantity.
Can Be Negative
Displacement can be negative if the object moves in the opposite direction to the chosen positive direction.
Kinematic Equations
Constant velocity
Constant acceleration
Average velocity
Without time
Physics Tips
Choose a consistent coordinate system and positive direction
Displacement can be zero even if distance traveled is not
Use consistent units throughout your calculations
For free fall, use a = 9.81 m/s² (downward)
Understanding Displacement in Physics
What is Displacement?
Displacement is a vector quantity that describes the change in position of an object. Unlike distance, which measures the total path traveled, displacement only considers the straight-line distance between the starting and ending positions.
Key Characteristics
- •Vector quantity: Has both magnitude and direction
- •Path independent: Only depends on start and end positions
- •Can be zero: Even if the object has moved
- •Can be negative: Depending on chosen coordinate system
Displacement vs Distance
Example: A person walks 3 km east, then 4 km north.
Distance traveled: 3 + 4 = 7 km
Displacement: √(3² + 4²) = 5 km (northeast)
Applications
- •Calculating work done by forces
- •Analyzing projectile motion
- •GPS navigation systems
- •Engineering and robotics
Mathematical Formulations
For constant velocity motion
For constant acceleration
Using initial and final velocities