Final answer:
The speed of the rocket will decrease over time due to the acceleration of gravity. After one second, the speed of the rocket will be approximately 20.2 m/s. After two seconds, the speed will decrease further to approximately 10.4 m/s, and after six seconds, the speed will be approximately -28.8 m/s.
Step-by-step explanation:
To calculate the speed of the rocket after a certain time, we need to take into account the acceleration due to gravity. Since the rocket is fired straight up, the only force acting on it is gravity, which causes it to slow down as it goes higher. We can use the equations of motion to find the speed of the rocket at different times.
After one second, the rocket will have a positive velocity but less than the initial velocity. The speed of the rocket after one second can be found using the equation:
v = u + at
where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time.
In this case, the initial velocity (u) is 30 m/s and the acceleration (a) is -9.8 m/s^2 (due to gravity). Substituting these values, we get:
v = 30 + (-9.8)(1) = 30 - 9.8 = 20.2 m/s
Therefore, the speed of the rocket after one second is approximately 20.2 m/s.
Similarly, we can find the speed of the rocket after two seconds and six seconds:
After two seconds: v = 30 + (-9.8)(2) = 30 - 19.6 = 10.4 m/s
After six seconds: v = 30 + (-9.8)(6) = 30 - 58.8 = -28.8 m/s
Therefore, the speed of the rocket after two seconds is approximately 10.4 m/s and after six seconds is approximately -28.8 m/s.