does an object speed up or slow down when:
1. its velocity is positive (right) and its acceleration is positive (right)? I said it speeds up
2. its velocity is positive (right) and its acceleration is negative (left)? I said it slows down
3. its velocity is negative (left) and its acceleration is negative (left)? I said it slows down
what is the rational for this to happen and am I correct with my answers?
if the acceleration is in the same direction as the velocity, the object speeds up.
Otherwise, the acceleration opposes the velocity, so it slows down.
The first step in understanding whether an object speeds up or slows down in different scenarios is to consider the relationship between velocity and acceleration.
Velocity represents the rate of change of displacement, which is a vector quantity that includes both magnitude and direction. Acceleration, on the other hand, represents the rate of change of velocity. It is also a vector quantity.
Now, let's analyze each scenario you provided:
1. When the velocity is positive (to the right) and the acceleration is positive (to the right) as well, the object will indeed speed up. This happens because the acceleration in the same direction as the velocity increases the object's speed. For instance, if a car is already moving to the right and its acceleration is also to the right, it will gain speed.
2. In the situation where velocity is positive (to the right) but the acceleration is negative (to the left), the object will slow down. In this case, the acceleration and velocity are in opposite directions, causing the object to decelerate. For example, if a car is initially moving to the right and experiences an acceleration to the left, it will gradually lose speed.
3. When the velocity is negative (to the left) and the acceleration is negative (to the left) as well, the object will generally speed up. This might seem counterintuitive, but it happens because the object is moving in the negative direction, and the acceleration is reinforcing that negative movement. In this case, the negative values of both velocity and acceleration lead to an increase in the object's speed in the negative direction.
Therefore, your answers are correct for scenarios 1 and 3, but not for scenario 2. In scenario 2, the object will slow down.