Step 1: Understanding the Concept:
This problem involves an object undergoing uniform linear acceleration.
We need to calculate the total displacement given the initial conditions and the acceleration period.
Step 2: Key Formula or Approach:
The distance travelled can be found using the second kinematic equation of motion.
The formula is \( s = ut + \frac{1}{2}at^{2} \), where \(u\) is initial velocity, \(a\) is acceleration, and \(t\) is time.
Step 3: Detailed Explanation:
The given values from the problem are:
Initial velocity, \( u = 5 \text{ m/s} \).
Acceleration, \( a = 2 \text{ m/s}^{2} \).
Time interval, \( t = 6 \text{ s} \).
Now, we substitute these parameters into the formula:
\[ s = (5)(6) + \frac{1}{2}(2)(6)^{2} \]
\[ s = 30 + (1)(36) \]
\[ s = 30 + 36 = 66 \text{ m} \]
Step 4: Final Answer:
The distance travelled by the object during this period is 66 m.