Calculating Stopping Distance: A Practical Example Using Kinematic Equations

Evaluating the motion of a vehicle under braking is a critical aspect of understanding and ensuring road safety. This article will explore a specific scenario in which a car is applying brakes to stop. We'll employ basic kinematic equations to determine the distance the vehicle will travel before coming to a complete stop. This real-world example involves converting units from km/hr to m/s and applying the kinematic equation that relates displacement, initial velocity, final velocity, and acceleration.

Understanding the Scenario

The scenario details a car moving at an initial speed of 40 km/h. The brakes produce a uniform deceleration (acceleration) of -0.6 m/s2. The objective is to calculate the distance s the vehicle will travel before coming to a stop.

Converting Units to Meters/Second

The initial speed of the vehicle needs to be converted from kilometers per hour (km/hr) to meters per second (m/s). The conversion factor is straightforward:

u 40 km/hr 3.6 11.11 m/s

Applying Kinematic Equations

The kinematic equation that relates the final velocity, initial velocity, acceleration, and displacement is given by:

v 2 u 2 2 a s

Here, v 0 m/s (final velocity), u 11.11 m/s (initial velocity), and a -0.6 m/s2 (acceleration).

Substituting Values and Solving for Distance s

Substituting the values into the equation:

0 11.11 2 - 1.2 s

This simplifies to:

0 123.4561 - 1.2 s

Rearranging the equation to solve for s:

1.2s 123.4561 → s 123.4561 1.2

Thus, s ≈ 102.88 meters.

Alternative Calculations and Considerations

Another approach to solving the problem involves:

Direct Calculation Method

Using the direct calculation method:

s 10000/81 -1

The result is s ≈ 123.45 meters.

Time Calculation Method

The time taken to stop can also provide an alternative method:

Given the deceleration of -0.6 m/s2 and initial velocity of 11.11 m/s, the time to stop can be calculated as:

t 11.11 0.6 ≈ 18.52 seconds

Using the distance under acceleration formula:

x 0.6 2 t 2 - 11.11 t 240.054 meters

This distance can be rounded to 240 m.

Conclusion

Using the provided kinematic equations, we determined that a car moving at 40 km/h with a deceleration of -0.6 m/s2 will travel approximately 102.88 to 123.45 meters before coming to a complete stop. These calculations highlight the importance of understanding the principles of motion in ensuring road safety.