Which of the following relations representing displacement x (t) of particle describes motion with constant acceleration?

Correct Answer - C
Acceleration `a=(d^(2)x)/(dt^(2))`
When a second order derivative of displacement `x(t)` w.r.t. to time, does not depend on time then the particle describes a motion with constant acceleration.
In option `(a)x=6-7t^(-2)`
`therefore(dx)/(dt)=-14t^(-3) thereforea=(d^(2)x)/(dt^(2))=42t^(-4)`
In option (a), acceleration varies with time, thereforea particle does not move with constant acceleration. In option (b) `x=3t^(2)+5t^(3)+7`
`therefore(dx)/(dt)=6t+15t^(2)`
`(dx)/(dt)=-14t^(-3) thereforea=(d^(2)x)/(dt^(2))=42t^(-4)`
In option (b), acceleration varies with time, therefore a particle does not move with constant acceleration.
In option (c) `x=9t^(2)+8`
`therefore(dx)/(dt)=18t therefore a=(d^(2)x)/(dt^(2))=18`
In option (c), acceleration does not vary with time, therefore a particle move with constant acceleration. In option (d) `x=4t^(-2)+3t^(-1)`
`therefore(dx)/(dt)=-8t^(-3)-3t^(-3) thereforea=(d^(2)x)/(dt^(2))=24t^(-4)+6t^(-3)`
In option (d), acceleration vary with time, therefore a particle does not move with constant acceleration.