8. lissette is driving to meet her family in a neighboring city. she accelerates at a constant rate and then…

8. lissette is driving to meet her family in a neighboring city. she accelerates at a constant rate and then maintains this speed for a period of time. an increase in traffic causes her to decelerate at a constant rate. lisette then reaches a constant speed and maintains this rate until she exits the highway. sketch a graph to represent the situation.

8. lissette is driving to meet her family in a neighboring city. she accelerates at a constant rate and then maintains this speed for a period of time. an increase in traffic causes her to decelerate at a constant rate. lisette then reaches a constant speed and maintains this rate until she exits the highway. sketch a graph to represent the situation.

Answer

Explanation:

Step1: Analyze acceleration phase

When accelerating at a constant rate, the speed - time graph is a straight line with a positive slope. Let the (y) - axis be speed ((v)) and the (x) - axis be time ((t)). If the initial speed (v_0 = 0) (assuming she starts from rest), and the acceleration (a>0), the equation of the line is (v=at) (for the acceleration phase).

Step2: Analyze constant - speed phase

When maintaining a constant speed, the slope of the speed - time graph is (0). So, it is a horizontal line. If the speed after acceleration is (v = v_1), the equation of this part of the graph is (v = v_1) (for the time interval of constant - speed).

Step3: Analyze deceleration phase

When decelerating at a constant rate, the slope of the speed - time graph is negative. Let the deceleration be (a_2<0). If the initial speed of this phase is (v_1) and the final speed after deceleration is (v_2), the equation of the line is (v=v_1 + a_2t) (for the deceleration phase).

Step4: Analyze final constant - speed phase

After deceleration, when maintaining a new constant speed (v = v_2), the graph is again a horizontal line until she exits the highway.

Answer:

The graph has four distinct parts:

  1. A straight line with a positive slope (acceleration).
  2. A horizontal line (constant speed).
  3. A straight line with a negative slope (deceleration).
  4. A horizontal line (new constant speed until exit).