Final answer:
The car's velocity on a position vs. time graph is represented by the slope of the tangent line to its path. If the car is moving with constant velocity, as indicated by a linear equation y = (2.0 km/min) x + 0, the tangent line will never be parallel to the time-axis which implies that there is no point in time at which the car's velocity is zero.
Step-by-step explanation:
To find at what time t the line tangent to the path of the car is parallel to the time-axis, we must understand that when a line is parallel to the time-axis on a position vs. time graph, the velocity of the object is zero, meaning there is no change in position over time. The car's velocity is represented by the slope of the tangent line to its path on the graph. Therefore, we need to find when the car has zero velocity.
From the provided information, we can deduce that the initial position of the car is 2.0 km west of the traffic light at t = 0, and it's 5.0 km east of the light at t = 6.0 min. Using these positions, we can calculate the average velocity of the car from t = 0 to t = 6 min, which is (5 km - (-2 km)) / (6 min - 0 min) = 7 km / 6 min. This average velocity indicates a constant velocity motion since the problem doesn't specify acceleration.
However, if we investigate a situation where the car could change its velocity, we need to look for the point at which the slope of the tangent equals zero. If the car's position is described by a quadratic equation, such as x(t) = 4.0 - 2.0t2m (a hypothetical example), to find when the car crosses the origin, we'd set x(t) to 0 and solve for t; however, to find when the velocity is zero, we'd take the derivative of x(t) with respect to t, set it to zero, and solve for t.
Given the linear equation y = (2.0 km/min) x + 0, which can also be written as x(t) = (2.0 km/min) t + 0, the slope of this line is constant at 2.0 km/min, meaning the car is always moving at a constant velocity and the line will never be parallel to the time-axis.