A few antiderivative application problems

**Problem 1**

A car starts from rest at time t = 0 and accelerates at -0.6t + 4 meters/sec^{2} for 0__<__t__<__12. How long does it take for the car to go 100 meters?

here is my work:

**Problem 2**

A 727 jet needs to attain a speed of 200 mph to take off. If it can accelerate from 0 to 200 mph in 30 seconds, how long must the runway be? (Assume constant acceleration and give your final answer in feet)

here is my work:

200 miles per hour = ft/sec

ft/sec divided by 30 sec = ft/sec

ft/sec

ft/sec

ft/sec

ft.

Please check the conversions and overall answer.

**Problem 3**

On the moon, the acceleration due to gravity is about 1.6 m/sec (compared to m/sec on earth). If you drop a rock on the moon (with initial velocity 0), find formulas for:

(a) Its velocity, v(t), at time t.

(b) The distance, s(t), it falls in time t.

here is my work:

m/sec

m/sec

(a) m/sec

(b) , where K is the initial height.

Should I keep the constant K in this answer? and how about the constants in all the other problems? I'm confused whether I need them or not.. In the previous ones I assumed the initial values were 0. Can I do this?