Final answer:
No, a car traveling in a straight line eastward cannot have accelerated northward because acceleration includes direction, not just speed changes. The acceleration is always in the direction of the velocity change, and in this case, it would be east, not north.
Step-by-step explanation:
A car that has only been traveling at different speeds in a straight line east cannot have accelerated north. Acceleration is a vector quantity that not only measures the rate of change of velocity but also the direction of that change. Since the car has only been moving eastward, any acceleration it experiences would be along that eastward direction, not to the north. Additionally, if the car is moving at a constant speed in a single direction, there is no acceleration; acceleration occurs only if there is a change in speed or direction. To further clarify, if a position vs time graph of an object that is speeding up was a straight line, this would indicate no acceleration, which is false. Constant acceleration is indicated by a curved displacement vs time graph. Moreover, when displacement vs time squared is plotted for constant acceleration, a straight line is expected, which is true.
Regarding displacement, two persons walking different paths but the same eastward and northward distances will end up at the same point, thus their displacements would be the same, making any claim that one has more displacement than the other false. If a person walks in the opposite direction than intended, the total magnitude of his displacement will not be the sum of the two distances; rather, it will be smaller due to the vectors partially canceling each other out.