A speedboat moves on a lake with initial velocity vector v1, x = 8.57 m/s and v1, y = - 2.61 m/s, then accelerates for 6.67 seconds at an average acceleration of aav, x = - 0.105 m/s2 and aav, y = 0.101 m/s2. What are the components of the speedboat/'s final velocity, v2, x and v2, y?

Find the speedboat's final speed?

First, you find the velocity at each component. The general equation is:

a = (v2 - v1) / t

a, x = (v2, x - v1, x) / t

-0.105 = (v2, x - 8.57) / 6.67

v2, x = 7.87 m/s

a, y = (v2, y - v1, y) / t

0.101 = (v2, y - - 2.61) / 6.67

v2, y = - 1.94 m/s

To find the final speed, find the resultant velocity by taking the hypotenuse.

v^2 = (v2, x) ^2 + (v2, y) ^2

v^2 = (7.87) ^2 + (-1.94) ^2

v = 8.1 m/s