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