If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters) after t seconds is given by H = 10t - 1.86t2. Find Velocity after 2 seconds. Find velocity of rock when x=a. When rock hits surface?

An expression for the velocity can be obtained by differentiating the distance term with respect to time. Therefore

dH/dt = v = 10 - 3.72t

substituting t = 2 sec

v = 10 - 3.72 (2)

v = 2.56 m/s, velocity after 2 hours

Since there is no variable x in the problem, I assumed that x = t = a

therefore at t = a

v = 10 - 3.72a^2

when the rock hits the surface:

when the rock reaches the top, the velocity is equal to zero

therefore the expression becomes, H = 1.86t2

dH/dt = v = 3.72t

when the rock hits the surface H = 10 therefore t = 2.32 s

@t = 2.32 s

v = 3.72*2.32 = 8.63 m/s