If a rock is thrown upward on the planet mars with a velocity of 14 m/s, its height (in meters) after t seconds is given by h = 14t − 1.86t2. (a) find the velocity of the rock after two seconds.

We have equation of motion , [tex]s= ut+\frac{1}{2} at^2[/tex], s is the displacement, u is the initial velocity, a is the acceleration and t is the time.

Here height of rock in meters, h = [tex]14t-1.86t^2[/tex]

Comparing both the equations

We will get initial velocity = 14 m/s(already given) and [tex]\frac{1}{2} a = -1.86[/tex]

So, Acceleration, a = -3.72 [tex]m/s^2[/tex]

Now we have equation of motion, v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration and t is the time taken.

When time is 2 seconds we need to find final velocity.

v = 14 - 3.72 * 2 = 6.56 m/s.

So, Velocity of rock after 2 seconds = 6.56 m/s