A motor scooter rounds a curve on the highway at a constant speed of 25.0 m/s. The original direction of the scooter was due east; after rounding the curve the scooter is heading 28 degrees north of east. The radius of curvature of the road at the location of the curve is 160 m.
What is the average acceleration of the scooter as it rounds the curve?
v^2/r
To find the average acceleration of the scooter as it rounds the curve, we need to determine the change in velocity and the time taken.
First, let's consider the change in velocity. The scooter started out traveling due east at a speed of 25.0 m/s. After rounding the curve, it is now heading 28 degrees north of east. To find the change in velocity, we can calculate the horizontal and vertical components of the velocity.
The horizontal component of the velocity remains unchanged because the scooter is still moving in the east direction. Therefore, the change in horizontal velocity is 0 m/s.
To find the change in vertical velocity, we can use trigonometry. Given that the original direction was east, and the new direction is 28 degrees north of east, we can form a right triangle. The vertical component of the velocity can be determined as:
Vertical velocity = 25.0 m/s * sin(28 degrees)
Now, we need to find the time taken. Since the speed of the scooter is constant throughout the curve, we can use the formula:
Time = Distance / Speed
The distance traveled along the curve is equal to the circumference of the circle with radius 160 m, given by:
Distance = 2 * pi * Radius
Therefore, the time taken would be:
Time = (2 * pi * 160 m) / 25.0 m/s
Finally, we can calculate the average acceleration using the formula:
Average acceleration = Change in velocity / Time taken
Substituting the values we obtained, we can find the average acceleration of the scooter as it rounds the curve.