Final answer:
The force must act on the mass for 16 seconds to raise its speed from 10 m/s to 12 m/s.
Step-by-step explanation:
To find the time it takes for a force to change the speed of an object, we can use the equation:
force x time = change in momentum
In this case, the force is 50 N, the change in momentum is (12 m/s - 10 m/s) x 400 kg = 800 kg m/s, and we need to find the time.
Using the equation, we can rearrange it to solve for time:
time = change in momentum / force
Plugging in the values, we have:
time = 800 kg m/s / 50 N = 16 s
Therefore, the force must act on the mass for 16 seconds to raise its speed from 10 m/s to 12 m/s.