# 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.

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