A particle is moving with the given data.

Question

Find the position of the particle.

a(t) = t² − 8t + 7,    s(0) = 0,    s(1) = 20

s(t) = 

 

Answer 1

Find the position of the particle.

a(t) = t² − 8t + 7,    s(0) = 0,    s(1) = 20

s(t) =  _t⁴/12 -4t³/3 +7t²/2 + 71t/4

we know integral of acceleration gives velocity,v, and integral of velocity gives displacement , s

∫(  t2 − 8t + 7 ) dt = t³/3 - 4t²+7t+ C₁

_{this means velocity of the particle , v=} t³/3 - 4t²+7t+ C₁

_{if we integrate it further we get the displacement , s∫}

_{∫ (} t³/3 - 4t²+7t+ C_{1 ) dt = t}⁴/12 -4t³/3 +7t²/2 + c₁t +c₂

_{given s(0) = 0 . when we substitue t=0 into the above eqution , we get} c₂= 0

given s(1)=20 , then 1⁴/12 - 4(1³)/3 + 7(1²)/2 +c₁(1)= 20

c₁= 71/4

the equation , s(t)= _t⁴/12 -4t³/3 +7t²/2 + 71t/4