22. the graphs in the accompanying figure show the position s, the
velocity v = ds/dt, and the acceleration a = d’s/ dtof a body
moving along a coordinate line as functions of time t. which graph
is which? give reasons for your answers.

A: a(t)

B: v(t)

C: s(t)

Step-by-step explanation:

One graph is position, s(t).

Another is velocity, v(t) = ds/dt (slope of the tangent line of the position curve).

The third is acceleration, a(t) = dv/dt (slope of the tangent line of the velocity curve).

If graph A is s(t), then velocity v(t) would always be positive.  No graph fits, so A is not s(t).

If graph B is s(t), then velocity v(t) would start negative then become positive, like graph A does.  If graph A is v(t), then acceleration a(t) would always be positive.  No graph fits, so A is not v(t), which means B is not s(t).

If graph C is s(t), then velocity v(t) would always be negative, like graph B.  If graph B is v(t), then acceleration a(t) starts negative then becomes positive, like graph A does.

Therefore:

A: a(t)

B: v(t)

C: s(t)