#### To determine

**To identify:** Each curves on the given graph and give proper explanation.

#### Answer

The curve *c* is position curve, *b* is velocity curve and *a* is acceleration curve.

#### Explanation

**Graph:**

The given graph is shown as in Figure 1,

**Observation:**

Observe the graph of *b* and *a* carefully.

The point where a(t)=0 is the same point where graph of b(t) has horizontal tangent.

Recall that the derivative of a function is zero where the function has a horizontal tangent.

Therefore, a(t) is the derivative of the graph b(t). That is, b′(t)=a(t).

Observe the graph of *a* and *c* carefully.

The graph of *a* has both positive and negative values. Hence *a* can be either velocity or acceleration.

The points where the graph of *a* has horizontal tangent, the functional value of *c* is not zero at that point.

This implies that, a′(t)≠c(t).

The only possibility is that *a* is the acceleration curve. This implies that c″(t)=a(t).

So, c″=b′=a′.

Thus, *c* is position curve, *b* is velocity curve and *a* is acceleration curve.