A particle travels along the curve from A to B


A particle travels along the curve from A to B in 2 s. It takes 4 s for it to go from B to C and then 3 s to go from C to D. Determine its average speed when it goes from A to D.

A particle travels along the curve from A to B

Image from: R. C. Hibbeler, K. B. Yap, and S. C. Fan, Mechanics for Engineers: Dynamics (SI Edition), 13th ed. Singapore: Pearson Education South Asia, 2013.

Solution:

We must first figure out the total distance traveled by the particle. To do so, we must realize that each curved section is in fact \frac{1}{4}th of the circumference of a circle. The length of each curved part is:

l_1=(\dfrac{1}{4})(2)(\pi)(10)=15.71 m

l_2=(\dfrac{1}{4})(2)(\pi)(5)=7.85 m

(Remember, the circumference of a circle is c=(2)(\pi)(r), where r is the radius)

 

The total distance the particle traveled = 15.71 + 15 + 7.85 = 38.56 m

 

Thus, the speed is:

speed=\dfrac{distance}{time}

speed=\dfrac{38.56}{2+4+3}=4.28 m/s

 

This question can be found in Engineering Mechanics: Dynamics (SI edition), 13th edition, chapter 12, question 12-80.

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