Answer :
Final answer:
The magnitude of the total acceleration of the race car just after it has begun to reduce its speed is 2.91 m/s².
Explanation:
To calculate the magnitude of the total acceleration of the race car, we can use the equation for centripetal acceleration:
a = v^2 / r,
where a is the acceleration, v is the velocity, and r is the radius of the curved part of the track.
First, we need to find the initial centripetal acceleration.
Using the given velocity of 46.4 m/s and radius of 302 m, the initial acceleration is:
a1 = (46.4 m/s)^2 / 302 m = 7.18 m/s2
Next, we need to find the final centripetal acceleration.
Using the given velocity of 35.9 m/s and radius of 302 m, the final acceleration is:
a2 = (35.9 m/s)^2 / 302 m = 4.27 m/s2
The magnitude of the total acceleration is the difference between the initial and final acceleration:
Total acceleration = |a1 - a2| = |7.18 m/s2 - 4.27 m/s2| = 2.91 m/s2