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A particle is moving along a straight line such that its acceleration can be given as a=3-4t, where t is in second. At t=0, its velocity is v=2m/s. Distance travelled by particle in 3 s is

A particle is moving along a straight line such that its acceleration can be given as a=3-4t, where t is in second. At t=0, its velocity is v=2m/s. Distance travelled by particle in 3 s is

Grade:11

1 Answers

Shailendra Kumar Sharma
188 Points
6 years ago
Now a=3-4t i.e dv/dt =3-4t => v= 3t-2t2 +C ; where C is a constant. given at t=0 v=2m/s so C=2. 
Now v = 3t-2t2 + 2 i.e. ds/sdt =3t-2t2 +2 => s =3t2/2-2t3/3+2t + K  now distance travelled in 3 sec will be given by s(3)-s(0)
Here s(3)-s(0)= 3*9/2-2*27/3+6+K -(0+0+0+K) =27/2-18+6 =1.5m
 

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