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A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v-t graph. Determine the total distance the motorcycle travels until it stops when t=15 s. Also plot the a-t and s-t graphs.

A motorcycle starts from rest at s = 0 and travels along a straight road with the speed shown by the v-t graph. Determine the total distance the motorcycle travels until it stops when t=15 s. Also plot the a-t and s-t graphs.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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**Problem 12-52: Kinematics of a Motorcycle** A motorcycle starts from rest at \( s = 0 \) and travels along a straight road. The speed is represented by the velocity-time (\( v-t \)) graph provided. The task is to determine the total distance the motorcycle travels until it comes to a stop at \( t = 15 \) seconds. Additionally, plot the acceleration-time (\( a-t \)) and position-time (\( s-t \)) graphs. **Graph Explanation:** The \( v-t \) graph is a piecewise linear graph divided into three segments: 1. **First Segment (0 to 4 seconds):** - The velocity increases linearly from 0 m/s to 5 m/s. - The equation governing this segment is \( v = 1.25t \). 2. **Second Segment (4 to 10 seconds):** - The velocity remains constant at 5 m/s. 3. **Third Segment (10 to 15 seconds):** - The velocity decreases linearly from 5 m/s to 0 m/s. - The equation for this segment is \( v = -t + 15 \). The \( v-t \) graph forms a trapezoidal shape, indicating three distinct phases of motion for the motorcycle: acceleration, constant velocity, and deceleration. **Steps to Solve:** 1. **Compute the Area under the \( v-t \) Graph:** - The total distance traveled is the area under the \( v-t \) graph. - Calculate the area for each segment and sum them. 2. **Plot the \( a-t \) and \( s-t \) Graphs:** - Use the slope of the \( v-t \) graph to determine acceleration (\( a \)). - Integrate the \( v-t \) graph to find the position over time for the \( s-t \) graph. This problem involves applying principles of kinematics to analyze the motion of the motorcycle through graphical representation and calculations.
Transcribed Image Text:**Problem 12-52: Kinematics of a Motorcycle** A motorcycle starts from rest at \( s = 0 \) and travels along a straight road. The speed is represented by the velocity-time (\( v-t \)) graph provided. The task is to determine the total distance the motorcycle travels until it comes to a stop at \( t = 15 \) seconds. Additionally, plot the acceleration-time (\( a-t \)) and position-time (\( s-t \)) graphs. **Graph Explanation:** The \( v-t \) graph is a piecewise linear graph divided into three segments: 1. **First Segment (0 to 4 seconds):** - The velocity increases linearly from 0 m/s to 5 m/s. - The equation governing this segment is \( v = 1.25t \). 2. **Second Segment (4 to 10 seconds):** - The velocity remains constant at 5 m/s. 3. **Third Segment (10 to 15 seconds):** - The velocity decreases linearly from 5 m/s to 0 m/s. - The equation for this segment is \( v = -t + 15 \). The \( v-t \) graph forms a trapezoidal shape, indicating three distinct phases of motion for the motorcycle: acceleration, constant velocity, and deceleration. **Steps to Solve:** 1. **Compute the Area under the \( v-t \) Graph:** - The total distance traveled is the area under the \( v-t \) graph. - Calculate the area for each segment and sum them. 2. **Plot the \( a-t \) and \( s-t \) Graphs:** - Use the slope of the \( v-t \) graph to determine acceleration (\( a \)). - Integrate the \( v-t \) graph to find the position over time for the \( s-t \) graph. This problem involves applying principles of kinematics to analyze the motion of the motorcycle through graphical representation and calculations.
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