If toy is switched on & allowed to travel in straight lines for 2 min, how many feet will it travel?

Question

The wheels of a toy car have a diameter of 3/pi inches. When the toy's motor is switched on, the wheels revolve 10 times per second. 

(these are the first parts of the question)

 

thanks for helping me!!

Answer 1

There's a slight mistake in Muhammad's answer.  His formula is right, but the units are wrong.  He's using revs/sec for angular velocity, but it should be radians/s.

 

Let's think of it like this:  When the wheel makes a full revolution, it has moved along the ground a distance equal to its circumference.  Using C = pi*d, we have C = pi * (3/pi) = 3 inches.  Since it revolves 10 times a second, the toy will move a total of 30 inches in a second. 

 

There are 60*2 = 120 seconds in 2 minutes, so the toy will have moved

120 seconds * (30 inches/ second) = 3600 inches in 2 minutes.  Multiply 3600 inches by (1 foot/12 inches) to get the answer of 300 feet.

Answer 2

Linear velocity = radius * angular velocity = (3/pi in.)(10/second) = 

 

30/pi in./sec

 

Distance = speed * time = (30/pi in/sec)(120 sec) = 3600/pi inches = 300/pi feet = 95.5 feet