The displacement s of a particle depends on time t according to the following relation s = 3 1 t 3 − t 2 + t . The velocity and displacement of the particle at the instant when its acceleration is z

Question

The displacement s of a particle depends on time t according to the following relation s = 3 1 ​ t 3 − t 2 + t . The velocity and displacement of the particle at the instant when its acceleration is zero, are respectively- ( A ∗ ) 0 , 3 1 ​

TestHub · Accepted Answer

The displacement is s = 3 1 ​ t 3 − t 2 + t . Velocity v = d t d s ​ = t 2 − 2 t + 1 . Acceleration a = d t d v ​ = 2 t − 2 . Set a = 0 : 2 t − 2 = 0 ⇒ t = 1 s. At t = 1 s: v = ( 1 ) 2 − 2 ( 1 ) + 1 = 0 m/s. s = 3 1 ​ ( 1 ) 3 − ( 1 ) 2 + 1 = 3 1 ​ − 1 + 1 = 3 1 ​ m. So, velocity is 0 and displacement is 3 1 ​ .

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