Question

Any help with these? I’ve tried to answer some but I’m really confused.

Answer 1

Top left: The slope of the line gives the (constant) acceleration of the moving object because the plot describes the velocity of some moving object. It's hard to tell what points the line passes through in the picture you took, but whatever slope/acceleration you find, that value will stay the same regardless of the time.

Top middle: The slope of the line is negative, which means acceleration has a negative sign. And because the line describes velocity over time, the fact that velocity is linear means that acceleration is constant.

Top right: The acceleration is the slope of the tangent line to the parabola at $t=10$. You can visually confirm that the slope of this line would be positive. Now, the average velocity between $t=10$ and $t=11$ is

$\bar a=\dfrac{v(11)-v(10)}{11-10}\approx16-14=2$

Judging by the plot, $2\,\dfrac{\mathrm m}{\mathrm s^2}$ seems like a pretty reasonable choice among the answers.

Bottom left: The slope of the tangent line at any point on the plot would be negative. Because velocity is non-linear, $a$ will not be constant.

Bottom middle: Opposite situation as in [bottom left].

Bottom right: The acceleration can only be negative for $t$, which means $t=2\,\mathrm s$ must be the correct answer.