Final answer:
The magnitude of the object's acceleration is 6 m/s², and the direction is to the west (opposite to its initial direction of travel, which is east).
Step-by-step explanation:
To determine the magnitude and direction of the object’s acceleration, we first need to calculate the change in velocity (Δv) and the time interval (Δt) during which this change occurred. The initial velocity (vi) is 74 m/s east, and the final velocity (vf) is 32 m/s east. Therefore, the change in velocity is Δv = vf − vi = 32 m/s − 74 m/s = −42 m/s. This indicates the object is slowing down. The time interval is Δt = 7.0 seconds.
To find the acceleration, use the formula a = Δv / Δt. Substituting the given values, a = (−42 m/s) / (7.0 s) = −6 m/s2. Since the change in velocity is negative, the acceleration is also in the negative direction with respect to the object's initial direction of travel, which is east. Hence, the acceleration of the object is 6 m/s2 to the west.