Starting from rest a particle moves in a straight line with acceleration a=(25−t2)1/2m/s2for0≤t≤5s a=3π8m/s2fort≥5s The velocity of particle at t = 7s is:
11 m/s
22 m/s
33 m/s
44 m/s
A
22 m/s
B
33 m/s
C
11 m/s
D
44 m/s
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Solution
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v=∫adt
a=(25−t2)1/2m/s2for0≤t≤5s =3π8m/s2fort≥5s
v=∫(25−t2)1/2dt+a0≤t≤5s =∫3π8dt+bt≥5s
v=t2√52−t2+252sin−1(t5)+a0≤t≤5s =3πt8+bt≥5s
at t=0,v=0 gives a=0
finding b using the fact that speed is a continous fuction
limt→5−v=limt→5+v
0+252sin−1(55)=3π×58+b
b=35π8
v=t2√52−t2+252sin−1(t5)0≤t≤5s =3πt8+35π8t≥5s
so at t=7
v=3π×78+35π8
v=8π×78
v=7π
v=22m/s
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