Final answer:
The total acceleration of an object moving in a circular path is the vector sum of its centripetal acceleration and tangential acceleration. The magnitude of the total acceleration can be found using the formula a = sqrt(a_c^2 + a_t^2), where a_c is the centripetal acceleration and a_t is the tangential acceleration.
Step-by-step explanation:
The total acceleration of an object moving in a circular path is the vector sum of its centripetal acceleration and tangential acceleration. The centripetal acceleration is given by the formula ∆v^2/r, where ∆v is the change in velocity and r is the radius of the circular path. The tangential acceleration is given by the formula a_t = rα, where a_t is the tangential acceleration and α is the angular acceleration. The magnitude of the total acceleration can be found using the formula a = sqrt(a_c^2 + a_t^2), where a_c is the centripetal acceleration and a_t is the tangential acceleration.
In this case, since the car is already in motion and accelerating, we can assume that the tangential acceleration is non-zero. We are given the angular speed (0.640 rad/s) and the angle between the total acceleration and the radius (29.3°). To find the magnitude of the total acceleration, we can use the properties of right triangles. The tangential acceleration is the side adjacent to the angle, and the centripetal acceleration is the side opposite to the angle. Using the given values, we can calculate the magnitude of the total acceleration.