Question

a car, initially traveling 12m/s averages 19m/s, while increasing speed steadily.
determine all unknowns.
|v₀| = m/s
|v̄| = m/s
|v_f| = m/s

Explanation:

Step1: Identify initial velocity

Initial velocity \( |v_o| = 12 \, \text{m/s} \) (given).

Step2: Identify average velocity

Average velocity \( |\bar{v}| = 19 \, \text{m/s} \) (given).

Step3: Calculate final velocity

Use average velocity formula: \( \bar{v} = \frac{v_o + v_f}{2} \). Rearrange: \( v_f = 2\bar{v} - v_o = 2(19) - 12 = 26 \, \text{m/s} \).

Answer:

\( |v_o| = 12 \, \text{m/s} \)
\( |\bar{v}| = 19 \, \text{m/s} \)
\( |v_f| = 26 \, \text{m/s} \)