22. The graphs in the accompanying figure show the position s, thevelocity v = ds/dt, and the acceleration a = d’s/ dtof a bodymoving along a coordinate line as functions of time t. Which graphis which? Give reasons for your answers.
Accepted Solution
A:
Answer: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)