Deceleration Time Calculator

The Deceleration Time Calculator computes the time it takes for an object to decelerate to a given final velocity from an initial velocity, using a specified deceleration rate. This tool is helpful for physics calculations, vehicle braking analysis, or motion control systems. The calculator provides results in seconds, minutes, and hours, accommodating various applications.

Calculator

1. enter the initial velocity of the object and select the velocity unit you want to use in your calculation
2. the final velocity of the object, and the calculation unit
3. the deceleration rate and choose either a Metric or Imperial unit
4. decimal precision, the number of digits after the decimal point

Results

1. the time of deceleration in seconds
2. deceleration time in minutes
3. deceleration time in hours

Formula:

The deceleration time is calculated using the formula:

\[ t = \frac{v_0 - v}{a} \]

Where:

• \(t\): Time (seconds)
• \(v_0\): Initial velocity (m/s, ft/s, km/h, mph)
• \(v\): Final velocity (m/s, ft/s, km/h, mph)
• \(a\): Deceleration rate (m/s², ft/s²)

Example Calculation:

Scenario: A car decelerates from an initial velocity of \(72 \, \text{km/h}\) to a final velocity of \(18 \, \text{km/h}\), with a deceleration rate of \(2 \, \text{m/s²}\). What is the deceleration time?

Step 1: Convert velocities to metres per second:

\[ v_0 = 72 \, \text{km/h} \div 3.6 = 20 \, \text{m/s} \] \[ v = 18 \, \text{km/h} \div 3.6 = 5 \, \text{m/s} \]

Step 2: Apply the formula:

\[ t = \frac{v_0 - v}{a} = \frac{20 - 5}{2} = \frac{15}{2} = 7.5 \, \text{s} \]

Step 3: Convert the result to minutes and hours:

\[ t_{\text{minutes}} = \frac{t}{60} = \frac{7.5}{60} = 0.125 \, \text{min} \] \[ t_{\text{hours}} = \frac{t_{\text{minutes}}}{60} = \frac{0.125}{60} = 0.00208 \, \text{hr} \]

Result:

• Deceleration time in seconds: \(7.5 \, \text{s}\)
• Deceleration time in minutes: \(0.125 \, \text{min}\)
• Deceleration time in hours: \(0.00208 \, \text{hr}\)