It looks like you've uploaded an image showing a graph of the position of a particle as a function of time, with a question asking where the instantaneous velocity and acceleration are less than zero.

Let me first describe how to interpret the graph and answer the questions:

1. Instantaneous velocity is the slope of the position-time graph. If the slope is positive, the velocity is positive; if the slope is negative, the velocity is negative.
2. Instantaneous acceleration is the rate of change of velocity. If the slope of the velocity-time graph is decreasing (i.e., the curve is concave down), acceleration is negative.

Where is the instantaneous velocity less than 0?

For the instantaneous velocity to be less than 0, we need to identify the regions of the graph where the slope is negative.

• From points D to E, the slope is negative, which means the velocity is less than 0 in this region.

Where is the instantaneous acceleration less than 0?

For acceleration to be negative, the velocity must be decreasing (the graph of the position function should be concave down).

• Between B and C, the slope is decreasing, so the acceleration is negative.
• Between E and F, the slope is increasing but concave down, so the acceleration remains negative in this region as well.

Answer summary:

• Instantaneous velocity less than 0: Between points D and E.
• Instantaneous acceleration less than 0: Between points B and C and E and F.

Would you like a further explanation on these concepts or help solving another part? Let me know!

Here are five questions related to this:

1. What is the definition of velocity in terms of position and time?
2. How can you determine when acceleration is positive on a position-time graph?
3. What is the significance of zero velocity in motion analysis?
4. How would the graph change if the particle had constant acceleration?
5. What are the differences between instantaneous and average velocity?

Tip: Remember, the steeper the slope, the greater the velocity (positive or negative).