Question

14 a student is walking home from school. the student first walks 20 meters towards their house at a velocity of 2 m/s. then the student sees a friend and stops where they are to talk to them for 30 seconds. the student then jogs 15 meters the rest of the way to their house at 5 m/s.
a. sketch a position vs. time graph for the situation above.
b. sketch a velocity vs. time graph for the situation above.
c. sketch an acceleration vs. time graph for the situation above.

1. two students walk 25 meters home from school. student a starts slow and then gets faster. student b starts fast and then gets slower. who gets home first?

Explanation:

Step1: Analyze part (a)

For the first - part of the motion (walking 20 meters at 2 m/s), using the formula $t=\frac{d}{v}$, the time taken $t_1=\frac{20}{2}=10$ s. The position increases linearly with a slope of 2 from $t = 0$ to $t = 10$ s. Then the student stops for 30 s, so the position remains constant from $t=10$ s to $t = 40$ s. For the last part (jogging 15 meters at 5 m/s), the time taken $t_2=\frac{15}{5}=3$ s. The position increases linearly with a slope of 5 from $t = 40$ s to $t=43$ s.

Step2: Analyze part (b)

For the first 10 s, the velocity is a constant 2 m/s. For the next 30 s, the velocity is 0 m/s. For the last 3 s, the velocity is a constant 5 m/s.

Step3: Analyze part (c)

During the first 10 s, since the velocity is constant, the acceleration is 0 m/s². During the 30 - s stop, the acceleration is 0 m/s². When the student starts jogging, there is an instantaneous acceleration from 0 to 5 m/s in a very short time (assumed instantaneous for simplicity), and then a constant 0 m/s² acceleration while jogging at a constant speed.

Step4: Analyze part (15)

The area under the velocity - time graph represents the displacement. Since both students have the same displacement (25 meters). Student B starts with a higher velocity. Even though Student B slows down and Student A speeds up, because Student B has a head - start in terms of initial velocity and covers a significant part of the 25 - meter distance at a high speed, Student B gets home first.

Answer:

a. The position - time graph has three segments: a line with a slope of 2 from $t = 0$ to $t = 10$ s, a horizontal line from $t = 10$ s to $t = 40$ s, and a line with a slope of 5 from $t = 40$ s to $t = 43$ s.
b. The velocity - time graph has three segments: a horizontal line at $v = 2$ m/s from $t = 0$ to $t = 10$ s, a horizontal line at $v = 0$ m/s from $t = 10$ s to $t = 40$ s, and a horizontal line at $v = 5$ m/s from $t = 40$ s to $t = 43$ s.
c. The acceleration - time graph has three segments: a horizontal line at $a = 0$ m/s² from $t = 0$ to $t = 10$ s, a horizontal line at $a = 0$ m/s² from $t = 10$ s to $t = 40$ s, an instantaneous spike (assumed) at $t = 40$ s and then a horizontal line at $a = 0$ m/s² from $t = 40$ s to $t = 43$ s.

1. Student B gets home first.