Question

if velocity is positive, which would most likely yield a negative acceleration? a final velocity that is faster than an initial velocity. a time that is less than a half hour. an initial velocity that is faster than a final velocity. a time that is greater than a half hour.

Explanation:

Acceleration is defined as the change in velocity over time, \(a=\frac{v_f - v_i}{t}\), where \(v_f\) is final velocity, \(v_i\) is initial velocity, and \(t\) is time. Negative acceleration (deceleration) occurs when the final velocity is less than the initial velocity (since \(v_f - v_i\) will be negative, and time \(t\) is positive).

• Option A: If \(v_f>v_i\), \(v_f - v_i\) is positive, so acceleration is positive. Eliminate.
• Option B: Time duration (less than half - hour) doesn't determine the sign of acceleration, as acceleration depends on velocity change. Eliminate.
• Option C: If \(v_i>v_f\), then \(v_f - v_i\) is negative. Since time \(t\) is positive, \(a=\frac{v_f - v_i}{t}\) will be negative (negative acceleration). This is correct.
• Option D: Time duration (greater than half - hour) doesn't determine the sign of acceleration, as acceleration depends on velocity change. Eliminate.

Answer:

C. An initial velocity that is faster than a final velocity.