### Physics Problem: Catching Up with a Speeder**Problem Statement:**A car is speeding at 25 m/s (constant) in a school zone. A police car starts from rest just as the speeder passes and accelerates at a constant rate of 5.0 m/s². How fast is the police car traveling when it catches up with the speeder?**Analysis Steps:**1. **Identify Given Data:** - Speed of the speeder: \( v_s = 25 \, \text{m/s} \) (constant) - Initial speed of the police car: \( v_{p0} = 0 \, \text{m/s} \) - Acceleration of the police car: \( a_p = 5.0 \, \text{m/s}^2 \)2. **Determine the time it takes for the police car to catch up:** - The distance traveled by the speeder in time \( t \): \[ d_s = v_s \cdot t \] - The distance traveled by the police car in time \( t \): \[ d_p = \frac{1}{2} a_p \cdot t^2 \] - Set \( d_s = d_p \) to find \( t \): \[ v_s \cdot t = \frac{1}{2} a_p \cdot t^2 \] \[ 25 \cdot t = \frac{1}{2} \cdot 5.0 \cdot t^2 \] \[ 25t = 2.5t^2 \] \[ t = \frac{25}{2.5} = 10 \, \text{seconds} \]3. **Calculate the final velocity of the police car:** - Use the equation of motion: \[ v_p = v_{p0} + a_p \cdot t \] \[ v_p = 0 + 5.0 \cdot 10 = 50 \, \text{m/s} \]**Answer:**When the police car catches up with the speeder, it is traveling at a speed of \( 50 \, \

Given data- speed of car v=25 m/s. Police car starts from rest (u=0 m/s) and accelerates at a…

A car is speeding at 25 m/s (constant) in a school zone. A police car starts from rest just as the speeder passes and accelerates at a constant rate of 5.0 m/s². How fast is the police car traveling when it catches up with the speeder?

A car is speeding at 25 m/s (constant) in a school zone. A police car starts from rest just as the speeder passes and accelerates at a constant rate of 5.0 m/s². How fast is the police car traveling when it catches up with the speeder?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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