To find the time it took for the beam to reach a speed of 22 m/s, we can use the equation of motion:
v = u + at
where:
- v is the final velocity (22 m/s),
- u is the initial velocity (0 m/s as the beam starts from rest),
- a is the acceleration (given as 3 m/s^2), and
- t is the time taken.
We can rearrange the equation to solve for t:
t = \frac{{v - u}}{{a}}
Substituting the given values:
t = \frac{{22 \, \text{m/s} - 0 \, \text{m/s}}}{{3 \, \text{m/s}^2}}
Simplifying:
t = \frac{{22 \, \text{m/s}}}{{3 \, \text{m/s}^2}}
Therefore, the time it took for the beam to reach a speed of 22 m/s is:
t = 7.3 \, \text{s}
Answer: \boxed{7.3 \, \text{s}}