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Question:

The position of a particle as a function of time t is given by x(t) = at + bt^2 - ct^3 where a, b, and c are constants. When the particle attains zero acceleration, then its velocity will be?

a+b22c

a+b2c

a+b23c

a+b24c

Solution:

Correct option is D. a + b²/3c
x = at + bt² - ct³
v = dx/dt = a + 2bt - 3ct²
a = dv/dt = 2b - 6ct = 0 => t = b/3c
v(at t = b/3c) = a + 2b(b/3c) - 3c(b/3c)² = a + b²/3c.