A race car entering the curved part of the track drops its speed from 46.4 m/s to 35.9 m/s in 2.56 s. If the radius of the curved part of the track is 302 m, calculate the magnitude of the total acceleration, in m/s², of the race car just after it has begun to reduce its speed.

Question

High School

Answer :

ishuraj00008 ishuraj00008 · Answer 1 · 2024-08-08T12:24:23-04:00

The magnitude of the total acceleration of the race car just after it has begun to reduce its speed is 2.91 m/s².

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