Final answer:
The position vs time graph of an object that is speeding up is curved, not a straight line, which is False. Displacement vs time squared for constant acceleration is a straight line, which is True. Average speed can be greater than average velocity if there's a change in direction, so the statement is False.
Step-by-step explanation:
The position vs time graph of an object that is speeding up is not a straight line. Therefore, the answer to this question is b. False. When an object is speeding up, this indicates that it has a non-zero acceleration. The position vs time graph for an accelerating object is a curve, specifically a parabola if the acceleration is constant. When acceleration is involved, the slope (or steepness) of the graph changes over time, which is what produces the curvature.
Considering an object moving with constant acceleration, the plot of displacement versus time is indeed a curved line due to the continuous change in velocity. This makes the first statement in the second question True. The plot of displacement versus time squared will be a straight line if the acceleration is constant, also making the second statement True. The mathematical basis for this comes from the kinematic equations for uniformly accelerated motion, where displacement can be expressed as a function of time squared.
Regarding the average speed versus average velocity, the average speed is calculated as the total distance traveled divided by the time, while the average velocity is the displacement (the straight-line distance from start to finish) divided by time. If the path taken involves any change in direction, the distance traveled will be greater than the displacement, hence the average speed could be greater than the average velocity, making the statement False.
It is True that we can use the Pythagorean theorem to calculate the length of the resultant vector obtained from the addition of two vectors which are at right angles to each other. This is a fundamental principle in vector addition.
Moreover, it is True that a vector can form the shape of a right-angle triangle with its x and y components. We often resolve a vector into its perpendicular components (using trigonometry) when analyzing forces, velocities, or other vector quantities in physics.