Calculating Distance Traveled by Mrs. V: A Case Study on Accelerated Rolling Blading

Mrs. V started rollerblading from rest and accelerated at a rate of 1.12 m/s2 for 13 seconds. This article delves into the physics behind her motion, exploring the concepts of time, velocity, and distance covered during this interval.

Understanding Accelerated Motion

Accelerated motion, or uniformly accelerated motion, is a fundamental concept in physics. When an object experiences a constant acceleration, its velocity changes at a steady rate. For Mrs. V, this means that her velocity increases by 1.12 m/s every second.

Calculating Final Velocity

Given her initial velocity ( u 0 ) m/s, the final velocity (( v )) can be calculated using the formula:

( v u at )

( v 0 1.12 times 13 ) m/s

( v 14.56 ) m/s

Calculating Average Speed and Distance Traveled

The average speed can be determined by using the formula for average velocity:

( v_{avg} frac{v u}{2} )

( v_{avg} frac{14.56 0}{2} 7.28 ) m/s

Multiplying this average speed by the time interval (( t )) will give us the distance traveled:

( d v_{avg} times t )

( d 7.28 times 13 94.64 ) meters

Alternative Calculation Method

Another method to calculate the distance traveled can be done using the formula for distance under constant acceleration:

( s ut frac{1}{2} at^2 )

( s 0 times 13 frac{1}{2} times 1.12 times 13^2 )

( s frac{1}{2} times 1.12 times 169 )

( s frac{1}{2} times 189.68 )

( s 94.64 ) meters

Displacement and Velocity Change

The displacement of Mrs. V can also be calculated using the formula for second-degree displacement:

( s frac{v^2 - u^2}{2a} )

( s frac{(14.56)^2 - (0)^2}{2 times 1.12} )

( s frac{211.9936}{2.24} )

( s 94.64 ) meters

This confirms that the distance traveled by Mrs. V during the 13-second acceleration period is 94.64 meters.

Conclusion

By understanding the principles of accelerated motion, we can accurately calculate the distance Mrs. V traveled while rollerblading. This example demonstrates the importance of fundamental physics concepts in solving real-world problems, such as sports and athletics.