Understanding the Concepts

* Acceleration: A change in velocity over time.

* Constant Acceleration: The acceleration remains the same throughout the motion.

* Initial Velocity: The starting velocity (in this case, 0 miles per second since the train is stationary).

Formula

We can use the following equation of motion:

* v = u + at

Where:

* v is the final velocity

* u is the initial velocity

* a is the acceleration

* t is the time

Calculations

1. Convert acceleration to miles per second: The acceleration is given as 0.5 miles per second. This is a very high acceleration (and unrealistic for a train). Let's assume it's a typo and it's actually 0.5 *miles per second squared* (miles/s²).

2. Plug in the values:

* u = 0 miles/second

* a = 0.5 miles/s²

* t = 15 seconds

3. Solve for v:

* v = 0 + (0.5 miles/s²)(15 seconds)

* v = 7.5 miles/second

Answer

The speed of the train after 15 seconds is 7.5 miles per second.