To tackle this problem, we need to carefully analyze the velocity-time graph (speed diagram) and use it to find the required kinematic information. Here's a structured approach to solve each part:

Given Data:

• $t = 0$: $x(0) = -1$ m
• We’ll interpret specific values from the velocity-time graph to solve the problem.

Solutions:

1. Calculating the Position of the Mobile at $t = 1$ s and $t = 4$ s

To find the position at $t = 1$ s and $t = 4$ s, we use the relationship between velocity and displacement: $x(t) = x(0) + \int_{0}^{t} v(t) \, dt$ We need to interpret the area under the velocity curve between $t = 0$ s and $t = 1$ s, and between $t = 0$ s and $t = 4$ s. Positive areas represent displacement in the positive $x$-direction, while negative areas indicate displacement in the opposite direction.

2. Total Distance Traveled and Average Scalar Speed in the First 4 Seconds

The distance is the sum of absolute values of the areas under the curve from $t = 0$ s to $t = 4$ s. To find the average speed, use: $\text{Average speed} = \frac{\text{Total distance traveled}}{\text{Total time}} = \frac{\text{Total distance}}{4 \, \text{s}}$

3. Average Velocity Between $t = 1$ s and $t = 4$ s

The average velocity over the interval from ( t = 1 \