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Displacement Calculator

Enter the values and click the 'Calculate' button to determine the displacement (distance traveled) of an object from its starting point.

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Displacement Calculator

Use this displacement calculator to find the change in position of an object. It lets you calculate displacement under various conditions of motion using different formulas:

  • If the displacement is based on average velocity (v) over a constant time (t):

S = v × t

  • If the displacement involves initial velocity (u) and constant acceleration (a) over time (t):

S = u t + ½ a t²

  • If the displacement assumes constant acceleration with initial and final velocities (u and v) over time (t):

S = ½ (v + u) t

What is Displacement?

"Displacement is the shortest distance an object travels in a straight line from its starting point to its ending point."

It represents the change in position of an object, considering both magnitude and direction.

  • Quantity: Vector
  • SI Unit: meter (m)

Example: A car moves 20 meters east, then 10 meters west. The total distance traveled is 30 meters (20 + 10), but the displacement is 10 meters east, as this is the net change in position.

Displacement of an object

How to Calculate Displacement

Example 1:

If a car moves with an average velocity of 40 m/s for 120 s, the displacement is:

S = v × t = 40 × 120 = 4800 m

Example 2:

A body starts from rest and reaches a velocity of 80 m/s after 30 s. Assuming constant acceleration:

  • Initial velocity u = 0 m/s
  • Final velocity v = 80 m/s
  • Time t = 30 s

S = ½ (v + u) t = ½ (80 + 0) × 30 = 1200 m

Example 3:

A car has an initial velocity of 20 m/s and acceleration 2 m/s² for 15 s. Find displacement:

  • Initial velocity u = 20 m/s
  • Acceleration a = 2 m/s²
  • Time t = 15 s

S = u t + ½ a t² = 20 × 15 + ½ × 2 × 15² = 300 + 225 = 525 m

Difference Between Displacement & Distance

Feature Distance Displacement
Definition Total length of the path traveled Straight-line path from start to end
Direction No Yes
Quantity Scalar Vector
Possible values Always positive or zero Positive, negative, or zero
Path dependence Depends on actual path Independent of path
Measurement Along any path Straight line from start to end
Example Car drives a curvy route for 10 km Person walks 4 steps east, then 4 steps west → displacement 0 km

Applications of Displacement Calculator

  • Physics: Solve problems in linear motion (1D)
  • Navigation: Find the direct route and compass heading between two points
  • Engineering: Support calculations of object motion in engineering systems
  • Everyday Use: Estimate direct distance covered, useful for walking, travel, or sports activities

FAQs

How do I calculate displacement without time?

Measure the final and initial positions, then subtract:

d = |x₂ - x₁|

Can displacement be greater than distance?

No. Displacement is always equal to or less than the total distance traveled by an object.

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