Question

Displacement of an object is related to time as x = at + bt² - ct³ where a, b and c are constants of motion. The velocity of the object when its acceleration is zero is given by ........... .
(A) a + b²/c
(B) a + b²/2c
(C) a + b²/3c
(D) a + b²/4c

Answer 1

Answer:

a + b²/3c

Explanation:

Displacement of an object is related to time as

x = at + bt² - ct³

Velocity = dx/dt  = a + 2bt  - 3ct²

acceleration = dv/dt = d²x/dt²  = 2b - 6ct

acceleration is zero  => 2b - 6ct = 0

=> b - 3ct = 0

=> t = b/3c

Velocity at t = b/3c

a + 2bt  - 3ct²

= a + 2b²/3c  - 3cb²/9c²

= a + 2b²/3c - b²/3c

= a + b²/3c

Answer 2

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