A particle travels along a straight line with a velocity of v=(20-o.o5s^2)m/s, where s is in meters. Determine the acceleration of the particle at s=15m.

v = 20  - 0.05s²

 

acceleration is given as a = dv/dt = -0.1s.ds/dt

 

where ds/dt = v

 

thus, a = -0.1s.v = -0.1s(20-0.05s²) = -2s + 0.005s³

at s = 15 m

the acceleration would be, a = -30 + 16.875 = -13.125 m/s²