Math Problem Statement

vf = vi + at

If you accelerate to vf = 5.9, accelerating at a = 1.4 m/s2 for t = 4.2 s, what was your initial velocity vi? Give answer to one decimal place.

Solution

To find the initial velocity viv_i, we can rearrange the formula:

vf=vi+atv_f = v_i + at

Solving for viv_i:

vi=vfatv_i = v_f - at

Now, substitute the given values:

  • vf=5.9m/sv_f = 5.9 \, \text{m/s}
  • a=1.4m/s2a = 1.4 \, \text{m/s}^2
  • t=4.2secondst = 4.2 \, \text{seconds}

vi=5.9(1.4×4.2)v_i = 5.9 - (1.4 \times 4.2)

vi=5.95.88=0.02m/sv_i = 5.9 - 5.88 = 0.02 \, \text{m/s}

So, the initial velocity viv_i is approximately 0.0m/s0.0 \, \text{m/s}.

Would you like more details on how the formula was derived or on another concept?


Here are 5 related questions for further exploration:

  1. How would the result change if the acceleration were doubled?
  2. What would be the distance traveled during this time?
  3. How does the direction of acceleration affect initial velocity?
  4. Can the equation be applied to non-constant acceleration scenarios?
  5. What happens to viv_i if the time duration is reduced?

Tip: Always keep track of the units when working with equations in physics to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Kinematics
Linear Motion

Formulas

vf = vi + at
vi = vf - at

Theorems

Newton's Second Law of Motion (implied in the acceleration)

Suitable Grade Level

Grades 9-12