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Question

# Starting from rest a particle moves in a straight line with accelerationa=(25−t2)1/2m/s2 for 0≤t≤5sa=3π8m/s2 for t≥5sThe velocity of particle at t = 7s is:

A
11 m/s
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B
22 m/s
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C
33 m/s
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D
44 m/s
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Solution

## The correct option is B 22 m/sv=∫adta=(25−t2)1/2m/s2 for 0≤t≤5s =3π8m/s2 for t≥5sv=∫(25−t2)1/2dt+a 0≤t≤5s =∫3π8dt+b t≥5sv=t2√52−t2+252sin−1(t5)+a 0≤t≤5s =3πt8+b t≥5sat t=0,v=0 gives a=0finding b using the fact that speed is a continous fuctionlimt→5−v=limt→5+v0+252sin−1(55)=3π×58+bb=35π8v=t2√52−t2+252sin−1(t5) 0≤t≤5s =3πt8+35π8 t≥5sso at t=7 v=3π×78+35π8 v=8π×78 v=7πv=22m/s

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