Question

. Displacement (x) and time (t) of a particle in motion are related as x = at+ bt² -ct³ where a, b and c are constants. The velocity of the particle when its acceleration becomes zero is

Answer 1

x = a t + b t^2 − c t^3
v = dx/dt = a + 2bt − 3ct^2
a(t) = dv/dt = 2b − 6ct

Set a(t)=0 ⇒ 2b − 6ct = 0 ⇒ t = b/(3c).

Then v = a + 2b(b/3c) − 3c(b/3c)^2 = a + (2/3)(b^2/c) − (1/3)(b^2/c)
= a + b^2/(3c).