Final answer:
Velocity vs. time graph for uniform acceleration is a straight line, acceleration calculated using the formula a = (Vf - Vi) / t. The acceleration during the first 8 seconds is 1 m/s², and during the last 6 seconds it is -1 m/s².
Step-by-step explanation:
To graph the velocity of a car accelerating at a uniform rate from 7.0 m/s to 12.0 m/s in 2.0 s, plot a velocity vs. time graph where the time axis (x-axis) spans at least 2 seconds and the velocity axis (y-axis) spans from 7.0 m/s to 12.0 m/s. The graph will be a straight line starting at the point (0, 7.0) and ending at the point (2.0, 12.0) since the acceleration is uniform.
To calculate the acceleration (a), use the formula a = (Vf - Vi) / t, where Vf is the final velocity, Vi is the initial velocity, and t is the time taken for the change in velocity. Substituting the given values, we get a = (12.0 m/s - 7.0 m/s) / 2.0 s = 2.5 m/s².
The acceleration of the car during the first 8 seconds (from 2 m/s to 10 m/s) is calculated by a = (Vf - Vi) / t = (10 m/s - 2 m/s) / 8 s = 1 m/s². During the last 6 seconds, when the car slows down from 10 m/s to 4 m/s, the acceleration is a = (4 m/s - 10 m/s) / 6 s = -1 m/s². Note the negative acceleration indicates a deceleration or slowing down.