Question:

A toy car is placed at the origin of a coordinate system and undergoes a series of motions as represented by the position-time graph shown below:

a) Describe the motion of the car from t = 0 s to t = 2 s. b) Calculate the average velocity of the car for the first 2 seconds. c) Determine the acceleration of the car from t = 2 s to t = 5 s. d) Sketch the corresponding velocity-time graph for the motion described by the position-time graph.

Answer:

a) From t = 0 s to t = 2 s, the motion of the car can be divided into three sections:

1. Constant positive velocity: From t = 0 s to t = 1 s, the slope of the position-time graph is constant, indicating constant positive velocity. The car is moving in the positive direction at a constant speed.

2. No motion: At t = 1 s, the position of the car remains constant, indicating that the car is at rest or not moving.

3. Constant negative velocity: From t = 1 s to t = 2 s, the slope of the position-time graph is negative, indicating constant negative velocity. The car is moving in the negative direction at a constant speed.

b) To calculate the average velocity of the car for the first 2 seconds, we can use the formula:

Average velocity = Δposition / Δtime

From t = 0 s to t = 1 s, the position changes from 0 m to 10 m, Δposition = 10 m. From t = 0 s to t = 2 s, the position changes from 0 m to -10 m, Δposition = -10 m. Δtime = 2 s - 0 s = 2 s.

Average velocity = (-10 m - 10 m) / 2 s = -20 m / 2 s = -10 m/s.

Therefore, the average velocity of the car for the first 2 seconds is -10 m/s.

c) To determine the acceleration of the car from t = 2 s to t = 5 s, we need to find the slope of the velocity-time graph for that time interval. Since the velocity-time graph represents the derivative of the position-time graph, the slope of the velocity-time graph gives the acceleration.

From t = 2 s to t = 5 s, the velocity remains constant at -10 m/s. Therefore, the acceleration during this interval is 0 m/s^2.

d) The velocity-time graph can be obtained by finding the slope of the position-time graph at different time intervals. Based on the position-time graph described, the corresponding velocity-time graph can be illustrated as:

Note that the velocity-time graph includes three distinct regions corresponding to the three different sections of the position-time graph described in part a).