Question

an object at rest corresponds with graph
an object moving in the positive direction with a constant speed corresponds with graph
an object moving in the negative direction with a constant speed corresponds with graph
an object that is accelerating in the positive direction, starting from rest corresponds with graph

Explanation:

Step1: Analyze object at rest

For an object at rest, its position $x$ does not change with time $t$. So the $x - t$ graph is a horizontal line. Graph B shows a horizontal line, so an object at rest corresponds to Graph B.

Step2: Analyze object moving in positive - direction with constant speed

The position - time relationship for an object moving with a constant speed $v$ in the positive direction is $x=x_0 + vt$ (where $x_0$ is the initial position), which is a linear function with a positive slope. Graph C has a positive - slope straight line, so an object moving in the positive direction with a constant speed corresponds to Graph C.

Step3: Analyze object moving in negative - direction with constant speed

The position - time relationship for an object moving with a constant speed $v$ in the negative direction is $x=x_0−vt$, which is a linear function with a negative slope. Graph A has a negative - slope straight line, so an object moving in the negative direction with a constant speed corresponds to Graph A.

Step4: Analyze object accelerating in positive direction starting from rest

The position - time relationship for an object starting from rest ($v_0 = 0$) and having a constant acceleration $a$ in the positive direction is $x=\frac{1}{2}at^{2}$, which is a parabola opening upwards. Graph D shows a curve that is a parabola - like shape opening upwards, so an object that is accelerating in the positive direction, starting from rest corresponds to Graph D.

Answer:

An object at rest corresponds with Graph B
An object moving in the positive direction with a constant speed corresponds with Graph C
An object moving in the negative direction with a constant speed corresponds with Graph A
An object that is accelerating in the positive direction, starting from rest corresponds with Graph D