Question

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.

Answer 1

Answer:

 Velocity of rock after 2 seconds = 6.56 m/s

Explanation:

 We have equation of motion , $s= ut+\frac{1}{2} at^2$, 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 = $14t-1.86t^2$

Comparing both the equations

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

     So,  Acceleration, a = -3.72 $m/s^2$

 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