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

compagnia04 2021-12-18 Answered
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 zero
v(t)=2th(tk2)4
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Expert Answer

levurdondishav4
Answered 2021-12-19 Author has 38 answers
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(t32)4dt
Now we will be solving the above integral :
s(t)=2t2(t32)4dt
s(t)=2t2(t32)4dt
We will take below substitution:
t32=u3t2dt=dut2dt=du3
t32=u3t2dt=dut2dt=du3
The integral becomes:
s(t)=23u3du
s(t)=2t2(t32)4dt
s(t)=2u515+C
Putting back the value of u, we get
s(t)=2(t32)515+C
where C is a constant
Now s(0)=0
This implies,
s(0)=2(022)515+C=0
0=2.2215+C
0=2615+C
2615=C
6415=C
Therefore, finally, we get
s(t)=2(t32)515

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abonirali59
Answered 2021-12-20 Author has 35 answers
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