Question

A rocket starting from its launch pad is subjected to a uniform acceleration of 100 meters/second2. Determine the time needed to reach the final velocity of 1,000 meters/second.

Answer 1

The velocity is the integral of acceleration.  If acceleration is 100 m/s^2 then velocity is:

$v= \int\limits^{}_{}100 \, dt=100t$

So to know the velocity at any time, t, we just put t in seconds into this equation.  To know at what time we get to a certain velocity, we set this equation equal to that velocity and solve for t:

$100t = 1000 \\ \\ t= \frac{1000}{100} =10s$