A particle’s acceleration is given by a(t) = 3. At t = 0, the particle is 7 units to the right of the origin and has a velocity of 3 units of distance per unit time to the right. Write an equation for s(t)?

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Answer 1 · 2018-05-08T09:14:49

#s(t)=3/2t^2+3t+7#

let's write down teh information given#

#a(t)=3#

if #v(t)= " the velocity at time "t#

we have

#t=0," "v(t)=+3" units of distance/unit time"--(1)#

#t=0" "s(t)=+7" units"--(2)#

now

#v(t)=inta(t)dt#

#v(t)=int3dt=3t+c_1#

using the initial conditions #(1)#

#3=3xx0+c_1#

#=>c_1=3#

#:. v(t)=3t+3#

#s(t)=intv(t)dt#

#s(t)=int(3t+3)dt#

#s(t)=3/2t^2+3t+c_2#

using initial conditions #(2)#

#7=0+0+c_2#

#=>c_2=7#

#:.s(t)=3/2t^2+3t+7#