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Problem: Some students used two straight segments and two half circles to make a track for a toy car, shown in the scale diagram at right. Each box on the diagram is 5 cm on a side.The car moves clockwise around the track at a constant speed. It takes the car 8 s to go around the track once.a. Determine the speed of the car. Show your work.b. Consider the interval that begins when the car passes point A and ends when the car passes point B (halfway around the track).i. On the diagram at right, draw an arrow to represent the direction of the average velocity over this interval. Explain your reasoning.ii. Determine the magnitude of the average velocity of the car over this interval. Show your work.iii. On the diagram at right, draw an arrow to represent the direction of the average acceleration over this interval. Explain your reasoning.iv. Determine the magnitude of the average acceleration of the car over this interval. Show your work.

FREE Expert Solution

Speed is calculated from:

Speed=DistanceTime

a.

We need to find the total distance of the track. 

We've been told that 1 box = 5 cm

Therefore, the length of the two segments is given by:

L = (2)(5)(4) = 40 cm

The length of two half circles is found from the circumference of a circle. 

Circumference, 

C=πD, where D is the diameter. 

D = (5)(4) = 20 cm

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Problem Details

Some students used two straight segments and two half circles to make a track for a toy car, shown in the scale diagram at right. Each box on the diagram is 5 cm on a side.
The car moves clockwise around the track at a constant speed. It takes the car 8 s to go around the track once.

a. Determine the speed of the car. Show your work.

b. Consider the interval that begins when the car passes point A and ends when the car passes point B (halfway around the track).

i. On the diagram at right, draw an arrow to represent the direction of the average velocity over this interval. Explain your reasoning.

ii. Determine the magnitude of the average velocity of the car over this interval. Show your work.

iii. On the diagram at right, draw an arrow to represent the direction of the average acceleration over this interval. Explain your reasoning.

iv. Determine the magnitude of the average acceleration of the car over this interval. Show your work.

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What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Uniform Circular Motion concept. You can view video lessons to learn Uniform Circular Motion. Or if you need more Uniform Circular Motion practice, you can also practice Uniform Circular Motion practice problems.

What professor is this problem relevant for?

Based on our data, we think this problem is relevant for Professor Clark's class at University of Maine.