A car travels in a flat circle of radius R. At a certain instant the velocity of the car is 24 m/s west, and the acceleration of the car has components of 2.4 m/s² east and 1.8 m/s² south. What is the radius of the circle? A) 0.24 km B) 0.19 km C) 0.32 km D) 0.14 km E) 0.27 km

Question

Quizplus · Accepted Answer

Since the car travels in a circle, its acceleration must be directed towards the center of the circle. To find the radius of the circle, we can use the following equation:

a = v^2 / R

where a is the magnitude of acceleration, v is the speed of the car, and R is the radius of the circle.

We can find the magnitude of acceleration by using the Pythagorean theorem:

a^2 = (2.4)^2 + (1.8)^2 
a = 2.98 m/s^2

Now we can use the equation to solve for R:

R = v^2 / a 
R = (24)^2 / 2.98 
R = 191.94 m

Converting to kilometers, we get:

R = 0.1919 km

Therefore, the best choice is C.

A Car Travels in a Flat Circle of Radius R