Question

A particle is moving with the given data. Find the position of the particle.A particle is moving with the given data. Find the position of the particle.
a(t) = t2 − 8t + 4,  s(0) = 0,  s(1) = 20
 
s(t)=_____________?

Accepted Answer

a(t) = t^2-8t+4
The derivative of velocity function v(t) is the acceleration function.
(dv(t))/dt = a(t) 
dv(t) = a(t)dt 
intdv(t) = inta(t)dt 
v(t) = inta(t)dt 
 
v(t) = int(t^2-8t+4)dt 
v(t) = t^3/3-4t^2+4t+C1 where C1 is a constant.
 
The derivative of position function is the velocity function.
(ds(t))/dt = v(t) 
ds(t) = v(t)dt 
intds(t) = intv(t)dt 
s(t) = intv(t)dt 
 
s(t) = int(t^3/3-4t^2+4t+C1)dt 
s(t) = t^4/12-4t^3/3+2t^2+C1t+C2 where C2 is a constant.
 
s(t) = t^4/12-4t^3/3+2t^2+C1t+C2
It is given that;
s(0) = 0 
 
s(1) = 20 
 
0 = 0^4/12-4*0^3/3+2*0^2+C1*0+C2 
0 = C2 
 
20 = 1^4/12-4*1^3/3+2*1^2+C1*1+0 
20 = 3/4+C1 
C1 = 77/4
 
So the position function is;
s(t) = t^4/12-(4t^3)/3+2t^2+(77t)/4

Math

A particle is moving with the given data. Find the position of the particle. A particle is moving with the given data. Find the position of the particle. a(t) = t2 − 8t + 4, s(0) = 0, s(1) = 20 s(t)=_____________?

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