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.

#### 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