Calculating the Time for a Bus to Travel 50 Meters with an Acceleration of 5m/s2

Have you ever wondered how long it takes for a bus that starts from rest to cover a distance of 50 meters under a constant acceleration of 5m/s2? This article will guide you through the step-by-step process using the kinematic equation, ensuring a thorough understanding of the physics involved. We'll also discuss some common misconceptions and clarifications related to units and vector aspects of acceleration.

Understanding the Problem

Let's start by summarizing the problem and the data we have:

Distance to be covered, d 50 meters Initial velocity, vi 0 m/s (since the bus starts from rest) Acceleration, a 5 m/s2 We need to find the time, t

Applying the Kinematic Equation

The kinematic equation for motion with constant acceleration, when the initial velocity is zero, is given by:

d a t2

Substituting the known values:

50 2

This simplifies to:

50 2.5 t2

Multiplying both sides by 2 to eliminate the fraction:

100 5 t2

Dividing both sides by 5:

20 t2

Finally, taking the square root of both sides:

t √20 ≈ 4.47 seconds

Therefore, the time taken to travel 50 meters is approximately 4.47 seconds.

Deriving the Same Result Using a Different Approach

Another way to solve this problem is by considering the area under the velocity-time graph for a straight line graph due to constant acceleration. The area under the graph represents the distance traveled. The formula for the area of a triangle is:

Area

Here, the height is the acceleration multiplied by time, and the base is the time itself. So:

d 2

Substituting the known values:

50 2

Following the same steps as before, we get:

t √20 ≈ 4.47 seconds

Misconceptions and Clarifications

It's worth noting some common misconceptions and clarifications related to acceleration and units:

Acceleration is the change of speed, not the speed itself. It is measured in meters per second squared (m/s2) or meters per square second, not m/s. Even though the bus is accelerating, the direction is not specified in the problem. For simplicity, we assume the bus is accelerating in a single direction. However, in more complex problems, the direction of acceleration can be significant.

Conclusion

By applying the kinematic equation and understanding the principles of constant acceleration, we can calculate the time it takes for a bus to travel a specific distance. It's also important to be aware of the correct units and to consider the direction when dealing with more complex scenarios.