A particle is moving along the path given by `y=(C )/(6)t^(6)` (where `C` is a positive constant). The relation between the acceleration (`a`) and the velocity (`v`) of the particle at `t=5sec` is

Options

A. `5a=v`
B. `a=5v`
C. `a=sqrt(v)`
D. `a=v`

Explanation

To solve the problem step by step, we will analyze the motion of the particle described by the equation \( y = \frac{C}{6} t^6 \), where \( C \) is a positive constant.

### Step 1: Find the velocity of the particle
The velocity \( v \) of the particle is given by the derivative of the position \( y \) with respect to time \( t \):
\[ v = \frac{dy}{dt} \]
Substituting the expression for \( y \):
...