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1D Kinematics Calculator (SUVAT)

Calculate displacement, final velocity, and average velocity for uniformly accelerated linear motion

Parameters

m/sⓘ
m/s²ⓘ
sⓘ
Show Trail

Controls

xⓘ

Calculated Values

Final Velocity:
13.00;m/s13.00;m/s
Displacement:
36.00;m36.00;m
Average Velocity:
9.00;m/s9.00;m/s
v² check (u² + 2as):
13.00;m/s13.00;m/s

Examples

Accelerating car

u = 0, a = 3 m/s² for 10 s.

  • Final Velocity: 30.0030.00
  • Displacement: 150.00150.00

Visualization

Understanding SUVAT (1D Kinematics)

One-dimensional kinematics describes motion along a straight line with constant acceleration a. The five SUVAT variables are: s (displacement), u (initial velocity), v (final velocity), a (acceleration), and t (time).

Four equations connect them; you need three known values to solve for a fourth. This calculator uses u, a, and t to find v and s—common in car acceleration, braking, and elevator problems.

v = u + at shows velocity changes linearly with time. Negative acceleration (deceleration) slows an object if it moves in the positive direction.

s = ut + ½at² gives displacement. The term ½at² is the extra distance gained due to acceleration beyond uniform motion at speed u.

Cross-check with v² = u² + 2as (no time) and s = ½(u + v)t. SUVAT fails when acceleration is not constant (e.g. air drag at high speed).

Key Concepts

  • v = u + at — velocity at time t
  • s = ut + ½at² — displacement in time t
  • v² = u² + 2as — links speed and distance without time
  • s = ½(u + v)t — average velocity × time
  • Sign convention: choose positive direction and stick to it
  • Constant a required; variable forces break SUVAT

Real-World Applications

  • Vehicle acceleration and braking distances
  • Elevator and conveyor belt motion
  • Sprinter starts and athletics timing
  • Class 11–12 mechanics numericals (NCERT, CBSE)
  • Introductory physics labs with motion sensors

Explore Further

More mechanics tools

Physics Equations

Final Velocity:
v=u+atv = u + at
Displacement:
s=ut+12at2s = ut + \frac{1}{2}at^2
Velocity-Displacement:
v2=u2+2asv^2 = u^2 + 2as

Step-by-Step Solution

See how the main results are calculated.

1

Identify SUVAT Variables

For uniform acceleration along a straight line, five quantities are linked by four SUVAT equations.

Equation:

u=initial velocity,  a=acceleration,  t=timeu = \text{initial velocity}, \; a = \text{acceleration}, \; t = \text{time}

Calculation:

u=5 m/s,a=2 m/s2,t=4 su = 5 \text{ m/s}, \quad a = 2 \text{ m/s}^2, \quad t = 4 \text{ s}

Result:

Known: u, a, t — find v and s

Explanation:

SUVAT applies only when acceleration is constant. Pick equations that avoid unknowns you do not need.

2

Calculate Final Velocity

Apply the velocity–time equation:

Equation:

v=u+atv = u + at

Calculation:

v=5+(2)(4)v = 5 + (2)(4)
v=5+8.00v = 5 + 8.00
v=13.00 m/sv = 13.00 \text{ m/s}

Result:

v=13.00 m/sv = 13.00 \text{ m/s}

Explanation:

Velocity changes linearly with time when acceleration is constant. Negative acceleration means slowing down if motion is positive.

3

Calculate Displacement

Apply the displacement–time equation:

Equation:

s=ut+12at2s = ut + \frac{1}{2}at^2

Calculation:

s=(5)(4)+12(2)(4)2s = (5)(4) + \frac{1}{2}(2)(4)^2
s=20.00+16.00s = 20.00 + 16.00
s=36.00 ms = 36.00 \text{ m}

Result:

s=36.00 ms = 36.00 \text{ m}

Explanation:

Displacement has a term from initial motion (ut) and a term from acceleration (½at²). Direction matters: s can be negative.

4

Cross-Check with v² = u² + 2as

Verify using the equation without time:

Equation:

v2=u2+2asv^2 = u^2 + 2as

Calculation:

v=u2+2as=52+2(2)(36.00)=13.00 m/sv = \sqrt{u^2 + 2as} = \sqrt{5^2 + 2(2)(36.00)} = 13.00 \text{ m/s}

Result:

v=13.00 m/s (matches)v = 13.00 \text{ m/s (matches)}

Explanation:

Average velocity s/t = 9.00 m/s also equals ½(u + v) = 9.00 m/s, confirming internal consistency.

Frequently Asked Questions (FAQ)

When do SUVAT equations fail?

When acceleration is not constant—for example, air drag at high speed or a force that varies with position.

Can displacement be negative?

Yes, if your positive direction is chosen one way and the object moves the other way, s is negative.

Which equation avoids time?

v² = u² + 2as relates velocity and displacement without needing t.

Why is average velocity (u + v)/2 valid here?

Only for uniform acceleration; then velocity changes linearly with time.

Practice MCQs

  1. If u = 0 and t doubles with same a, displacement becomes:
  2. Doubling acceleration (same u, t) changes displacement by:
  3. SUVAT requires:

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