A car moving at a speed of 54 km / h passes a highway curve with a radius of curvature of 250 m.

| April 29, 2021 | education

A car moving at a speed of 54 km / h passes a highway curve with a radius of curvature of 250 m. When cornering, the driver brakes the car, giving it an acceleration of 0.4 m / s2. Determine the normal and full acceleration of the vehicle.

V = 54 km / h = 15 m / s.
R = 250 m.
a = 0.4 m / s ^ 2.
a (norm) -?
a (gender) -?
Normal or centripetal acceleration is called the acceleration directed along the radius to the center of the circle and is determined by the formula: a (nor) = V ^ 2 / R. Where V is the speed of movement, R is the radius of curvature.
a (normal) = (15 m / s) ^ 2/250 m = 0.9 m / s ^ 2.
The total acceleration a (floor) will be the hypotenuse of a right-angled triangle: one of the legs of which is the normal acceleration a (norms) and the acceleration a. Find the total acceleration a (floor) by the Pythagorean theorem: a (floor) = √ (a (norm) ^ 2 + a ^ 2).
a (floor) = √ ((0.9 m / s ^ 2) ^ 2 + (0.4 m / s ^ 2) ^ 2) = 0.985 m / s ^ 2.
Answer: normal acceleration a (norm) = 0.9 m / s ^ 2, full acceleration a (floor) = 0.985 m / s ^ 2.



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