Math Problem Statement

If a vessel starts from rest and accelerates at a rate of 1.8 m/s2 for 60 seconds, calculate the speed of the vessel after the 60 seconds.

Solution

To calculate the speed of the vessel after 60 seconds, we can use the formula:

v=u+atv = u + at

Where:

  • vv is the final speed (which we need to find),
  • uu is the initial speed (since the vessel starts from rest, u=0u = 0),
  • aa is the acceleration (1.8m/s21.8 \, \text{m/s}^2),
  • tt is the time (60 seconds).

Substituting the values into the formula:

v=0+(1.8m/s2×60s)v = 0 + (1.8 \, \text{m/s}^2 \times 60 \, \text{s})

v=108m/sv = 108 \, \text{m/s}

So, the speed of the vessel after 60 seconds is 108m/s108 \, \text{m/s}.

Would you like more details or have any questions? Here are 5 related questions for further exploration:

  1. What is the distance traveled by the vessel during this time?
  2. How would the speed change if the acceleration was doubled?
  3. What would be the speed after 120 seconds at the same acceleration?
  4. How does acceleration relate to velocity in uniformly accelerated motion?
  5. What is the significance of "starting from rest" in this problem?

Tip: Always check if an object starts from rest, as it simplifies calculations by making the initial velocity zero.

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Math Problem Analysis

Mathematical Concepts

Kinematics
Uniform Acceleration
Linear Motion

Formulas

v = u + at

Theorems

First Equation of Motion

Suitable Grade Level

Grades 9-11