The motion of a particle moving the y-axis is represented as : y= 3 (t-2) +5 (t-2)^2. identify the correct statement (s)
A) The initial (t=0) velocity of a particle is 3m/s
B) The acceleration of a particle is 5m/s
C) The particle is at the origin at t=2s
D) All of these

A) Velocity v is given byv=dydt=10t-17so velocity at time t=0 is -17 m/sB) acceleration is given by a=d2ydt2=10 ms-2C) at time t=2, y=0. So the particle was at origin at time t=2. So statement C) is correct.

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differentiate it,
y=3(t-2) +5(t-2) 2
y=3t - 6+5( t2 - 4t + 4)
y=3t - 6 + 5t- 20t + 20
dy/dt = 3 - 0 + 10t - 20 + 0(velocity)....on putting t=0 we don't get 3
further differentiating...
which is not equal to 5
on putting t=2 directly in the initial question we get....position

y=0 therefore 3 is the correct answer

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