The displacement (in metres) of a particle varies with time (in second

1.	The displacement (in metres) of a particle varies with time (in seconds) ass(t) = 3t2-5t + 2Q2.I.II.III.Find the velocity of the particle at all instances when its displacement becomes zero.Find the acceleration of the particle when the velocity is 1 m/s.Find the displacement of the particle when it comes to rest momentarily.
Answer» given s(t) = 3t²-5t+2 = 0.... v(t) = ds/dt = 6t-5 1) for s(t) to be zero..=> 3t²-3t-2t+2 = 0=> 3t(t-1)-2(t-1) = 0=> (t-1)(3t-2) = 0=> t = 1, 2/3 so, the Velocity when displacement is 0V1 = 6(1)-5 = 1m/s and V2 = 6(2/3) -5 = -1m/s 2)a = dv/dt = 6 m/s²... always.. 3) when particle is at rest , velocity is 0so 6t-5 = 0 => t = 5/6 so, displacement is = 3(5/6)²-5(5/6)+2 = 2.08. -4.16+2 = 4.08-4.16 = 0.08 m

The displacement (in metres) of a particle varies with time (in seconds) ass(t) = 3t2-5t + 2Q2.I.II.III.Find the velocity of the particle at all instances when its displacement becomes zero.Find the acceleration of the particle when the velocity is 1 m/s.Find the displacement of the particle when it comes to rest momentarily.

Answer»

given s(t) = 3t²-5t+2 = 0.... v(t) = ds/dt = 6t-5

1) for s(t) to be zero..=> 3t²-3t-2t+2 = 0=> 3t(t-1)-2(t-1) = 0=> (t-1)(3t-2) = 0=> t = 1, 2/3

so, the Velocity when displacement is 0V1 = 6(1)-5 = 1m/s and V2 = 6(2/3) -5 = -1m/s

2)a = dv/dt = 6 m/s²... always..

3) when particle is at rest , velocity is 0so 6t-5 = 0 => t = 5/6

so, displacement is = 3(5/6)²-5(5/6)+2 = 2.08. -4.16+2 = 4.08-4.16 = 0.08 m