Question

Part A) Use the definition of linear speed to solve one of the four problems below. Show your work. Suppose that an object moves on a circle of radius r at a constant speed. If s is the distance traveled in time t on this circle, then the linear speed v of the object is defined as v=st .

1) An object is traveling around a circle with a radius of 7 feet. If in 40 seconds a central angle of 1/5 radian is swept​ out, what is the linear speed of the​ object?

2) An object travels a distance of 40 inches in 2.5 seconds as it moves along a circle of radius 2 ft. Find its linear speed over one minute.

3) A motorcycle travels at a constant speed around a track that is circular and has a circumference of 5 miles. If the motorcycle completes 5 laps in 12 minutes, what is the linear speed of the motorcycle in miles per hour?

4) A race car travels at a constant speed around a track that is circular and has a circumference of 4.4 miles. If the race car completes 7 laps in 10 minutes, what is the linear speed of the car in miles per hour?

Part B Create your own linear speed application problem for your classmates to solve.

Answer 1

Part A

1) Radius of circle. R = 7 feet

Angle travelled in 40 second,   = 1/5 radian

so distance travelled s = R X   = 7 X 1/5 = 1.4 feet

Linear speed = s/t = 1.4/40 = 0,035 feet/sec.

( As desired only one out of four problem is to be solved therefore problem no 1 of Part A is solved)

Part B

One idea of linear speed application problem is as given below :

Earth is revolving 2 radians (one lap) arround the sun in 24 hrs. Assume distance beween sun and earth to be  151 x 10 ⁶ km. Calculate the linear speed of earth.