Given the velocity v(t) of an object moving along a ccordinate line at time t, find the object's displacement s(t) moving along the coordinate line. The objects initial displacement is zerov(t)=2th(tk−2)4

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Given the velocity v(t) of an object moving along a ccordinate line at time t, find the object&#039;s displacement s(t) moving along the coordinate line. The objects initial displacement is zerov(t)=2th(tk−2)4

levurdondishav4 · Accepted Answer

s(t) is nothing but the integration of v(t) over time.  That is,  s(t)=∫v(t)dt  And intial displacement is given to be 0, which implies, s(0)=0  On taking h=2 and k=3 we have  s(t)=∫2t2(t3−2)4dt  Now we will be solving the above integral :  s(t)=∫2t2(t3−2)4dt  ⇒s(t)=2∫t2(t3−2)4dt  We will take below substitution:  t3−2=u⇒3t2dt=du⇒t2dt=du3  t3−2=u⇒3t2dt=du⇒t2dt=du3  The integral becomes:  s(t)=23∫u3du  ⇒s(t)=2∫t2(t3−2)4dt  ⇒s(t)=2u515+C  Putting back the value of u, we get  s(t)=2(t3−2)515+C  where C is a constant  Now s(0)=0  This implies,  s(0)=2(02−2)515+C=0  ⇒0=2.2215+C  ⇒0=2615+C  ⇒−2615=C  ⇒−6415=C  Therefore, finally, we get  s(t)=2(t3−2)515

abonirali59 · Accepted Answer

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Given the velocity v(t) of an object moving along a

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