Question

An automobile rolls down an incline, traveling s(t) = 3t2 + 7 feet in t seconds.

a) Find its velocity a t = 3. ft/sec

b) Find its acceleration at t = 3. [ft\sec^2]


c) After how many seconds will the velocity be 88 ft/sec? (seconds)

Answer 1

S(t)= 3t^2 + 7
1)If s is the length of the path travelled until time t,the speed equals the time derivative of s:
V(t)=ds/dt
V(t)=6t
if t=3 sec, V(3)=18 ft/sec
2) accelerationis the derivative of the velocity as a function on time
a(t)=dV/dt
a(3)=6 ftsec^2