The acceleration of an object is given as a function of posi

The acceleration of an object is given as a function of position in feet as a = 2 s^2 (ft/s^2). When s = 0, its velocity is v = 1 ft/s. What is the velocity of the object when s = 2 ft?

Solution

a = 2s^2

Vdv/ds = 2s^2

=> vdv = 2s^2ds

integrating both side

v2^2/2 - 1/2 = 2*2^2

=> v at s = 2ft = 4.12 ft/s