# Answer on Mechanics | Relativity Question for Adam

Question #33180

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)

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)

Expert's answer

S(t)= 3t^2 + 7

1)If

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

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

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