The displacement of a particle is expressed as

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

x(t)=p t^{3}+q t+r

, where

p, q, r

are constants. The particle is required to move with uniform velocity of

6\,\text{m/s}

for all time. Which one of the following pairs

(p, q)

(in SI units) satisfies this requirement? (a)

(2,\,0)

(b)

(1,\,6)

(c)

(0,\,6)

(d)

(-2,\,10)