**Problem Statement:**You are waiting at a traffic light on Manchester Expressway. At the instant the traffic light runs green, your car (a Toyota Rav4) that has been waiting at an intersection starts ahead with a constant acceleration of 3.17 m/s². At the same instant, a truck (a Ford Ranger), traveling with a constant speed of 20.2 m/s, overtakes and passes you. How far beyond the traffic light do you overtake the truck?**Your Answer:**[Answer Box]**Explanation:**This problem involves understanding and applying the principles of kinematics. Here we have two vehicles starting from the same point but with different motions:1. The Toyota Rav4 starts from rest and accelerates at a constant rate.2. The Ford Ranger travels at a constant speed.We'll need to set up equations that describe the motion of both vehicles and find the point at which the distances covered by the two vehicles are equal.**Approach:**1. **Toyota Rav4 (accelerating):** - Initial velocity (\( u \)) = 0 m/s (since it starts from rest) - Acceleration (\( a \)) = 3.17 m/s² - Distance traveled (\( s_{\text{car}} \)) after time (\( t \)) can be found using the equation: \[ s_{\text{car}} = ut + \frac{1}{2}at^2 \] \[ s_{\text{car}} = 0 + \frac{1}{2} \cdot 3.17 \cdot t^2 \] \[ s_{\text{car}} = 1.585 \cdot t^2 \]2. **Ford Ranger (constant speed):** - Constant speed (\( v \)) = 20.2 m/s - Distance traveled (\( s_{\text{truck}} \)) after time (\( t \)) is: \[ s_{\text{truck}} = v \cdot t \] \[ s_{\text{truck}} = 20.2 \cdot t \]3. **Equating the distances:** - Set the distance equations equal to find the time when the Toyota Rav4 overtakes the truck: \[ 1.585 \cdot t^2 = 20.2 \cdot t

Name: **Problem Statement:**You are waiting at a traffic light on Mancheste
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: **Problem Statement:**You are waiting at a traffic light on Manchester Expressway. At the instant the traffic light runs green, your car (a Toyota Rav4) that has been waiting at an intersection starts ahead with a constant acceleration of 3.17 m/s².