Understanding the Concepts

* Initial Velocity (v₀): The starting velocity of the object, which is 45 mph.

* Acceleration (a): The rate of change of velocity, which is -10 mph/sec (negative because it's decelerating).

* Time (t): The duration of the acceleration, which is 3 seconds.

* Final Velocity (v): The velocity of the object after the acceleration.

Formula

The equation that relates these quantities is:

v = v₀ + at

Calculations

1. Convert units: Since the acceleration is in mph/sec, we need to convert the initial velocity to mph/sec. There are 3600 seconds in an hour:

45 mph = 45 mph * (1 hour / 3600 seconds) = 0.0125 mph/sec

2. Plug in the values:

v = 0.0125 mph/sec + (-10 mph/sec) * 3 seconds

3. Calculate:

v = 0.0125 mph/sec - 30 mph/sec = -29.9875 mph/sec

Answer

The final velocity of the object is -29.9875 mph/sec. The negative sign indicates that the object is moving in the opposite direction from its initial motion.