Let be the trains path and be bills path.

(a)

The position at time of an object having acceleration is .

The acceleration of the train is .

Train:

.

.

Bill:

.

.

(b)

Bill will catch the train if .

.

Find .

.

Since , the equation has no real solution.

Thus, Bill will not catch the train.

(c)

Graph the parametric equations , , and .

(a)

Train: , .

Bill: , .

(b)

Bill will not catch the train.

(c)

Graph the parametric equations , , and .