Question

a car, initially traveling 30m/s averages 24m/s as it decreases speed steadily.
determine all unknowns.
|v₀| = m/s
|v̄| = m/s
|v_f| = m/s

Explanation:

Step1: Identify initial speed

Initial speed \(|v_o|\) is given as 30 m/s.

Step2: Identify average speed

Average speed \(|\bar{v}|\) is given as 24 m/s.

Step3: Calculate final speed

For steady (constant acceleration) motion, average speed \(\bar{v} = \frac{v_o + v_f}{2}\). Rearrange to find \(v_f\):
\(v_f = 2\bar{v} - v_o = 2(24) - 30 = 18\) m/s.

Answer:

\(|v_o| = 30\) m/s
\(|\bar{v}| = 24\) m/s
\(|v_f| = 18\) m/s