Calculating the Distance Traveled by a Bus with Given Initial Velocity and Acceleration

This article explains how to calculate the distance traveled by a bus when its initial velocity and acceleration are given. The solutions are derived using the SUVAT equations and the SUVRT equations. Additionally, we will provide an experimental based solution to validate the results.

Problem Statement

The bus starts with an initial velocity of 15 meters per second (m/s) and accelerates at a rate of 2 meters per second squared (m/s2) for 0.5 hours. How far did the bus travel?

Given Values

Initial velocity, u 15 m/s Acceleration, a 2 m/s2 Time, t 1800 seconds (0.5 hours times; 3600 seconds/hour) No. of reference points, n 1801

Solutions Using the SUVAT and SUVRT Equations

Let’s calculate the distance traveled by the bus using both the SUVAT (Constant Acceleration) and SUVRT (Variable Acceleration) equations.

Solution Using SUVAT Equations

The SUVAT equation for distance traveled is given by:

s ut 0.5at2

Substituting the given values:

s 15 times; 1800 0.5 times; 2 times; 18002

s 27000 360000

s 387000 meters

However, there seems to be an error in the problem statement as the time t 3060 seconds instead of 1800 seconds. Let’s use the correct time to find the correct distance traveled.

Solution with Corrected Time (3060 seconds)

The correct distance traveled using the SUVAT equations:

s 15 times; 3060 0.5 times; 2 times; 30602

s 45900 937020

s 982920 meters

Solution Using SUVRT Equations

According to the SUVRT equations, the distance traveled can be calculated using:

s 15n 2rt/60

Where n is the number of reference points, r is the acceleration in m/s, and t is the time in seconds.

Substituting the values:

s 15 times; 1801 2 times; 1800 / 60

s 27015 60

s 27075 meters

However, the provided solution seems to follow an alternate method and calculates the distance as:

s 15 times; 1801 1/2 times; 2 times; 18002

s 27015 3240000

s 3268815 meters

Experimental Based Solution

To experimentally validate the solution, we calculate the distance traveled in each time interval up to the 1800th second. The distances in each time interval increase linearly with a common difference of 2 meters. This can be expressed as an arithmetic series:

The series is: 17 19 21 ... 3615

The sum of the first n terms of an arithmetic series is given by:

Sn n/2 times; (2a (n-1) d)

In this case, a 17, d 2, and n 1800.

S1800 1800/2 times; (2 times; 17 (1800-1) times; 2)

S1800 900 times; (34 3598)

S1800 900 times; 3632

S1800 3268800 meters

Conclusion

The distance traveled by the bus, using the correct values, is 3268800 meters. This is confirmed by the experimental based solution.

Keywords: distance traveled, initial velocity, acceleration, SUVAT equations, SUVRT equations