The distance(s) in metres covered by a particle in motion at any time, t seconds, is given by S =120t - 16t\(^2\). Find in metres, the distance covered by the body before coming to rest.

A.

220

B.

222

C.

223

D.

225

Correct answer is D

s = 120t - 16t\(^2\) - 16t\(^2\)

\(\frac{ds}{dt} = 120 - 32t\)

120 - 32t = 0

\(\frac{32t}{32}\) = \(\frac{120}{32}\)

t = 3.75

s = 120(3.75) - 16(3.75)\(^2\)

= 450 - 225 

= 225