An automobile travels at a constant speed around a curve whose radius of curvature is 2000m. What is the maximum allowable speed if the maximum acceptable value for the normal scalar component of acceleration is 1.5m/s squared?

To find the maximum allowable speed of the automobile, we need to consider the relationship between the normal scalar component of acceleration and the maximum allowable speed in circular motion.

In circular motion, the normal scalar component of acceleration is given by the equation:

an = v^2 / r

where an is the normal scalar component of acceleration, v is the velocity of the automobile, and r is the radius of curvature.

In this case, the maximum acceptable value for the normal scalar component of acceleration (an) is given as 1.5 m/s^2, and the radius of curvature (r) is given as 2000 m.

We can rearrange the equation to solve for the maximum allowable speed (v):

v^2 = an * r

v = sqrt(an * r)

Now, let's substitute the given values into the equation:

v = sqrt(1.5 m/s^2 * 2000 m)

v = sqrt(3000 m^2/s^2)

v ≈ 54.77 m/s

Therefore, the maximum allowable speed for the automobile is approximately 54.77 m/s.