SUVAT Calculator

Displacement (s):

Initial Velocity (u):

Final Velocity (v):

1. What is a SUVAT Calculator (a and t)?

Definition: This calculator uses SUVAT equations to determine acceleration (a) and time (t) for uniformly accelerated motion, given displacement (s), initial velocity (u), and final velocity (v).

Purpose: It helps in physics and engineering to analyze motion by calculating how quickly an object accelerates and how long it takes.

2. How Does the Calculator Work?

The calculator uses these SUVAT equations:

\[ v^2 = u^2 + 2as \quad \text{(to calculate a)} \] \[ v = u + at \quad \text{(to calculate t)} \] Where:

\(s\): Displacement (m, km)
\(u\): Initial velocity (m/s, km/h)
\(v\): Final velocity (m/s, km/h)
\(a\): Acceleration (m/s², g)
\(t\): Time (s, min, hour)

Unit Conversions:

Displacement (s): m, km (1 km = 1000 m)
Velocity (u, v): m/s, km/h (1 km/h = 0.277778 m/s)
Acceleration (a): m/s², g (1 g = 9.81 m/s²)
Time (t): s, min, hour (1 min = 60 s, 1 hour = 3600 s)

Steps:

Enter displacement (s), initial velocity (u), and final velocity (v), selecting their units.
Convert inputs to base units (m, m/s).
Calculate acceleration (a) using \( a = \frac{v^2 - u^2}{2s} \).
Calculate time (t) using \( t = \frac{v - u}{a} \).
Convert results to selected units and display.

3. Importance of Calculating a and t

Calculating acceleration and time is crucial for:

Motion Analysis: Understanding how objects speed up or slow down.
Design: Optimizing systems like vehicles or roller coasters.
Safety: Ensuring safe stopping distances or travel times.

4. Using the Calculator

Examples:

Example 1: For \(s = 100 \, \text{m}\), \(u = 10 \, \text{m/s}\), \(v = 20 \, \text{m/s}\):
- Acceleration: \(a = \frac{20^2 - 10^2}{2 \times 100} = 1.5 \, \text{m/s²} = 0.153 \, \text{g}\)
- Time: \(t = \frac{20 - 10}{1.5} = 6.667 \, \text{s} = 0.002 \, \text{hour}\)
Example 2: For \(s = 0.5 \, \text{km}\), \(u = 0 \, \text{km/h}\), \(v = 36 \, \text{km/h}\):
- Convert: \(s = 500 \, \text{m}\), \(v = 10 \, \text{m/s}\)
- Acceleration: \(a = \frac{10^2 - 0^2}{2 \times 500} = 0.1 \, \text{m/s²} = 0.010 \, \text{g}\)
- Time: \(t = \frac{10 - 0}{0.1} = 100 \, \text{s} = 0.028 \, \text{hour}\)

5. Frequently Asked Questions (FAQ)

Q: What if displacement is zero?
A: The calculator cannot compute if \(s = 0\), as it leads to division by zero.

Q: What if acceleration is zero?
A: If \(v = u\), acceleration is zero, and time cannot be calculated this way.

Q: What is g?
A: \(g\) is the acceleration due to gravity, approximately 9.81 m/s².