Final answer:
To find the displacement of the car, we convert the initial velocity to m/s, determine the time to stop, and use the kinematic equation to calculate the total displacement, which is approximately 32.7 meters south.
Step-by-step explanation:
The question asks for the displacement of a car as it comes to a stop after the driver slams on the brakes. To solve this problem, we use the kinematic equation for displacement with constant acceleration (deceleration in this case), which is:
s = ut + (1/2)at², where s is the displacement, u is the initial velocity, t is the time, and a is the acceleration.
First, we convert the speed from km/h to m/s: 47 km/h = (47 × 1000) / (60 × 60) = 13.056 m/s. Next, we calculate the time taken to stop using v = u + at, where v is the final velocity (0 m/s, since the car stops). Rearranging for t gives us t = (-u) / a = (-13.056 m/s) / (5.2 m/s²) = 2.511 seconds. Finally, substituting into the displacement equation: s = (13.056 m/s × 2.511 s) + (1/2 × -5.2 m/s² × (2.511 s)²) = 32.7 m (approximately).
The car's displacement from the moment the driver slammed the brakes to when the car stopped is approximately 32.7 meters south.