If an object travels with positive velocity in the x-direction, can it have a negative acceleration along the x-axis at the same time?

(I think it can't both should be positive- because when you draw the velocity time graph - the gradient (acc.) is also positive) ???? =/

Positive velocity, negative acceleration. Happens every time I approach a red light on the highway, slowing down (deaccelerating)>

You are correct. An object that travels with positive velocity in the x-direction cannot have a negative acceleration along the x-axis at the same time.

To understand this, let's first clarify the meanings of velocity and acceleration. Velocity is the rate at which an object's position changes with respect to time. Acceleration, on the other hand, is the rate at which an object's velocity changes with respect to time.

If an object has a positive velocity in the x-direction, it means that it is moving to the right along the x-axis. This implies that its position is increasing over time.

Now, if the object has a negative acceleration along the x-axis, it means that its velocity is decreasing over time. In other words, the object is slowing down its motion in the x-direction.

If we consider the velocity-time graph, as you mentioned, the acceleration is represented by the gradient (slope) of the graph. Since the object has a positive velocity, the graph will have a positive slope. However, if the acceleration is negative, the slope of the graph will be negative, indicating that the object is slowing down.

Therefore, an object with positive velocity in the x-direction cannot have a negative acceleration along the x-axis simultaneously.