Question

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m/s² for 8.0 s. How far does the boat travel during this time?
1. 91 m
2. 96 m
3. 98 m
4. 99 m

Answer 1

Correct Answer - Option 2 : 96 m

The correct answer is 96 m

• Given, the initial velocity of the boat = 0 m/s
  • Acceleration of the boat = 3 m/s²
  • Time period = 8s
  • As per the second motion equation, s = ut + 1/2 at²
  • Therefore, the total distance traveled by boat in 8 seconds = 0 + 1/2 [(3) × (8)²]
  • s = 96 meters
  • Therefore, the motorboat travels a distance of 96 meters in a time frame of 8 seconds.

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• There are three equations of motion that can be used to derive components such as displacement(s), velocity (initial and final), time(t) and acceleration(a).
• The following are the three equation of motion:
  • First Equation of Motion: v = u + at
  • Second Equation of Motion: s = ut + 1/2(at2)
  • Third Equation of Motion: v2 = u2 + 2as