(a)

The height of the rock after seconds is .

Velocity at the surface of the Mars .

Velocity function is derivative of displacement function.

.

Velocity of rock after seconds is .

Velocity of rock after  seconds :

Velocity of rock after seconds is m/s.

(b)

The height is m.

Height of the rock is .

Since roots of the quadratic function  are .

Roots of the quadratic function  :

First root:

.

Second root:

.

Velocity of rock is .

Velocity at time .

At height  m the velocity of rock on its way up is .

Velocity at time .

Here negative sign indicates direction of motion is down wards.

At height m the velocity of rock on its way down is .

(a) Velocity of rock after seconds is m/s.

(b) The velocity of rock on its way up is  m/s.

     The velocity of rock on its way down is  m/s.