Final answer:
To calculate the linear acceleration of a car given the tire rotation speed and time, convert rev/s to rad/s, calculate the angular acceleration, and then use the tire's radius to find the linear acceleration.
Step-by-step explanation:
To find the linear acceleration of the car, we first need to understand the relationship between linear acceleration and angular acceleration since we are given the rotational speed of the car's tires. The formula connecting linear acceleration (a) and angular acceleration (alpha) is a = r * alpha, where r is the radius of the tire.
First, we calculate the angular acceleration. We're given that the car's tires are rotating at 20.5 revolutions per second (rev/s) after 21 seconds from rest. To get angular acceleration in rad/s², we convert revolutions per second to radians per second by multiplying by 2π (since one revolution equals 2π radians). Then we divide by the time to get angular acceleration:
alpha = (20.5 rev/s * 2π rad/rev) / 21 s = 20.5 * 2π / 21 rad/s²
Next, we convert the tire's diameter to radius by dividing by 2, so r = 24.9 cm / 2 = 12.45 cm = 0.1245 m. Now we can use the formula a = r * alpha to calculate the linear acceleration.
a = 0.1245 m * (20.5 * 2π / 21 rad/s²)
a = 0.1245 m * 20.5 * 2π / 21 rad/s² (Calculate this value for the final answer)
Perform the calculation to find the linear acceleration in meters per second squared (m/s²).