Problem 5. An object moves on a circular path such that its distance covered is given by the function: s = 0.512 m+21 m. The ratio of the magnitudes of its accelerations at times t 2s and t2 = 5s is 1:2. Find the radius of the circle.
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- Sophie is sitting in the stands, watching a car race around a circular track. The track has a radius of 68.0 meters, and the car passes Sophie approximately every 9.44 seconds. Based on these measurements, what is the car's speed? 31.9 m/s 50.1 m/s 29.0 m/s 45.3 m/sFind the magnitude of the instantaneous acceleration (in m/s²) of an object that moves at a constant speed around a circle if it take it 4.24 s to complete one revolution. The radius of the circle is 2.52 m.An object moves in a circular path at a constant speed. What is the relationship between the directions of the object's velocity and acceleration vectors? The velocity vector points in a direction tangent to the circular path. The acceleration is zero. The velocity and acceleration vectors are perpendicular. The velocity and acceleration vectors point in opposite directions. The velocity and acceleration vectors point in the same direction. The velocity vector points toward the center of the circular path. The acceleration is zero.
- A vehicle travels at a speed of 4 m/ sec along a horizontal Circular road that has a radius of 50m its speed is then increased by ú= (0.05.s) m/sec² for a short distance from S = 0, where s is in meters. Calculate the magnitude of its acceleration when it has moved s = 10m in ml sec².An airplane makes a gradual 270° turn (heading goes from north to west to south to east) while flying at a constant speed of 212 m/s and maintaining the same altitude. The process takes 15.6 seconds to complete and the radius of the turn is 2105 m. For this turn, the magnitude of the average acceleration of the plane is?The average distance of the earth from the sun is about 1.5 x 108 km (Figure 1). Assume that the earth's orbit around the sun is circular and that the sun is at the origin of your coordinate system. (a) Estimate the speed of the earth as it moves in its orbit around the sun. Express your answer in miles per hour with the appropriate number of significant figures. (b) Estimate the angle between the position vector of the earth now and what it will be in 4 months. (c) Calculate the distance between these two positions.
- A student drives 10 km to the north and then 20 km 30 degrees South of the east. By using the component method, what are the magnitude and direction of his displacement from the starting point?A group of hikers sets out going 10.0km [N], then 15.0km [E], then 4.0km [S]. The entire trip takes 4.00h. Determine the magnitude hikers' velocity for the trip. 4.04 km/h [N 21.8° E] 5.25 km/h [N 21.8° E] 7.25 km/h [N 21.8° E] 21.0 km/h [N 21.8° E] 65.25 km/h [N 21.8° E]Trent is running along a circular track that has a radius of 45 meters. Trent starts at the 3-o'clock position and travels in the CCW direction, stopping after 106 meters. Imagine an angle with a vertex at the center of the circular track that subtends the path Trent has traveled. When Trent stops, what is his horizontal distance from the center of the track?
- A bicyclist is at the bottom of a hill with a speed of 30 ft/s. After traveling 600 ft on the road, she reaches the top of the hill with a speed of 15 ft/s. Her total acceleration at the top of the hill is 1.3 ft/s^2. Assuming her acceleration along the road is constant. -What is the radius of curvature for the top of the hill?An object is traveling around the rim of a circular track whose diameter is 45.3 m. When it has rotated by 2π radians, what is its linear displacement (in centimeters)?A Ferris wheel with radius 8.5 m initially rotates clockwise at a constant rate by completing 1.25 rev in 40.00 s. It then begins to decelerate at a rate of 0.40 rad/s2 with its only passenger at the top of the wheel. Find the direction of the total acceleration vector. Express your answer as a positive number with respect to the positive x-axis. Choose up and to the right as your positive direction.