Final answer:
The car's acceleration, as it slows down from 45 miles/hour to rest in 3 seconds, is -6.7 m/s². This negative value indicates deceleration.
Step-by-step explanation:
To calculate the acceleration of a car that is slowing down from an initial velocity of 45 miles/hour to rest over the course of 3 seconds, we use the formula for acceleration: a = Δv / Δt, where Δv is the change in velocity, and Δt is the change in time. First, we need to convert the velocity from miles/hour to meters/second (m/s), since acceleration is measured in m/s². There are 1609.34 meters in a mile and 3600 seconds in an hour. So, 45 miles/hour is equal to 45 × 1609.34 / 3600 m/s, which simplifies to approximately 20.1 m/s.
The car comes to rest, so the final velocity (vf) is 0 m/s. The initial velocity (vi) is 20.1 m/s. Thus, the change in velocity (Δv) is vf - vi = 0 m/s - 20.1 m/s = -20.1 m/s (negative because the car is slowing down). The change in time (Δt) is given as 3 seconds.
The acceleration (a) is then calculated as follows: a = Δv / Δt = -20.1 m/s / 3 s = -6.7 m/s². The negative sign indicates that the acceleration is in the direction opposite to the velocity, which is expected since the car is decelerating.