# A particle travels along the curve

A particle travels along the curve from A to B in 1 s. If it takes 3 s for it to go from A to C, determine its average velocity when it goes from B to C.

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:

Let us first calculate the time it took the particle to go from B to C. We know that it took 1 second to go from A to B, and we know it took the particle 3 seconds to go from A to C. Thus, the particle took 3 – 1 = 2 seconds to go from B to C.

The average velocity can be found by finding the total distance between B and C and dividing it by the time. To do so, we will write it in vector form.

$v=\dfrac{\Delta r}{\Delta t}$

$v=\dfrac{r_{AC}-r_{AB}}{\Delta t}$

$v=\dfrac{40i-(20i+20j)}{2}$

$v=\left\{10i-10j\right\}$ m/s