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.



To find the initial velocity \( v_i \), we can rearrange the formula:

\[
v_f = v_i + at
\]

Solving for \( v_i \):

\[
v_i = v_f - at
\]

Now, substitute the given values:

- \( v_f = 5.9 \, \text{m/s} \)
- \( a = 1.4 \, \text{m/s}^2 \)
- \( t = 4.2 \, \text{seconds} \)

\[
v_i = 5.9 - (1.4 \times 4.2)
\]

\[
v_i = 5.9 - 5.88 = 0.02 \, \text{m/s}
\]

So, the initial velocity \( v_i \) is approximately \( 0.0 \, \text{m/s} \).

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

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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 \( v_i \) if the time duration is reduced?

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

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.

Find out how to calculate the initial velocity of an object when given the final velocity, acceleration, and time. Using the formula vf = vi + at, this physics problem covers essential concepts of kinematics and linear motion. Suitable for high school students (Grades 9-12).

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