fundamental theorem applications - calc

Question

The height of a rocket is a function of time, h(t), with h in meters and t in seconds. The rate of change of velocity is d2h/dt2 = t − 9.8 m/s2. The rocket is catapult launched, so that its velocity at time t = 0 is 50 m/s. Find a formula for velocity.

dh/dt= _____________

The catapult launches the rocket with an initial height of h(0) = 10 meters.

Find a formula for height.

h(t) = ____________

Answer 1

v(t) = ∫(t - 9.8)dt = t²/2 - 9.8t + C₁; v(0) = C₁ = 50;

v(t) = t²/2 - 9.8t + 50;

h(t) = ∫(t²/2 - 9.8t + 50)dt = t³/6 - 4.9t² + 50t + C₂;

h(0) = C₂ = 0.

h(t) = t³/6 - 4.9t² + 50t