Question

interpreting kinematics graphs
answer the questions 1 - 10 based on the graph of a remote - controlled car below. directions should be indicated as positive or negative signs on numerical values or, if specifically asked for direction, written as the words positive or negative.

1. what does the slope of the line in the graph above represent?
2. describe the motion of the remote - controlled car, including the direction, from t = 0 s to t = 4 s.
3. what is the velocity of the car at t = 9 s?
4. what is the direction (positive and/or negative) that the car is going at t = 9 s?
5. describe the direction of motion of the car at t = 11 s.
6. describe the motion of the car, including direction, from t = 12 s to t = 18 s.
7. what is the velocity of the car at t = 15 s?
8. what is the acceleration of the car at t = 15 s?
9. what is the velocity of the car at t = 18.5 s?
10. what is the total displacement of the car for the entire 20 - second period of time?

Explanation:

1.

Step1: Recall kinematics - slope concept

In a velocity - time graph, the slope represents acceleration. In a position - time graph, the slope represents velocity. Since the problem is about kinematics of a car and the slope of the line in a kinematics graph is being asked, if it is a velocity - time graph, slope = $\frac{\Delta v}{\Delta t}$ which is acceleration.

Step1: Analyze time interval

From $t = 0$s to $t=4$s, if the graph is a position - time graph and the slope is positive, the car is moving in the positive direction with a constant velocity (if the slope is constant). If it is a velocity - time graph and the value of velocity is positive, the car is moving in the positive direction and if the slope of the velocity - time graph is positive, it is accelerating in the positive direction.

Step1: Locate $t = 9$s on the graph

Find the value of the y - axis (velocity if it is a velocity - time graph) corresponding to $t = 9$s on the graph.

Answer:

Acceleration

2.