Question

in which of the following situations would a car be slowing down while traveling to the left? negative velocity and negative acceleration positive velocity and negative acceleration negative velocity and positive acceleration positive velocity and positive acceleration

Explanation:

To determine when a car moving left (negative direction, so negative velocity) slows down, we use the concept of velocity - acceleration direction:

• If velocity and acceleration have the same sign, the object speeds up. If they have opposite signs, the object slows down.
• The car is moving left, so velocity (\(v\)) is negative (\(v<0\)). For it to slow down, acceleration (\(a\)) must have the opposite sign of velocity (i.e., positive, \(a > 0\)), because when velocity and acceleration have opposite signs, the object is decelerating (slowing down).
• Let's analyze each option:
• Yellow (negative velocity, negative acceleration): Same sign, so speeding up (not slowing down).
• Purple (positive velocity, negative acceleration): Velocity is positive (moving right), but the car is moving left (so this is incorrect for direction).
• Orange (negative velocity, positive acceleration): Opposite signs, so slowing down (matches the situation).
• Teal (positive velocity, positive acceleration): Velocity is positive (moving right), not left (incorrect direction).

Answer:

orange. negative velocity and positive acceleration