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 calculated by the formula \(a=\frac{v_f - v_i}{t}\), where \(v_f\) is final velocity, \(v_i\) is initial velocity, and \(t\) is time. Negative acceleration (deceleration) occurs when the change in velocity (\(v_f - v_i\)) is negative (since time \(t\) is always positive).

• Option A: If \(v_f>v_i\), then \(v_f - v_i>0\), so \(a>0\) (positive acceleration), not negative.
• Option B: Time duration doesn't directly determine the sign of acceleration; it depends on velocity change. A time less than half an hour doesn't relate to velocity change direction.
• Option C: If \(v_i>v_f\), then \(v_f - v_i<0\). Since \(t>0\), \(a=\frac{v_f - v_i}{t}<0\) (negative acceleration).
• Option D: Similar to B, time greater than half an hour doesn't determine acceleration sign; it's about velocity change.

Answer:

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