How can an object have a negative acceleration while speeding up and a positive acceleration while slowing down? Please explain using easy terms, I do not understand the way my textbook explains it.

The sign before merely denotes direction, it has no relation whether the object is speeding or slowing.

A common misconception is that negative acceleration means the body is slowing, which is ##false##.

The ##+-## (+ or -) sign only tells you whether the motion is in the positive direction of the axis, or the negative direction.

If both velocity and acceleration have the same sign, the object is speeding. (Although note that there could be acceleration, but the object still has constant velocity, such as in uniform , I can explain this further if you want).

Here's a drawing I made to make it clearer:

In red, the acceleration has a negative sign, but the velocity is increasing, because it's also going along the acceleration.

In green, acceleration is positive but object is slowing.

I can explain this even further if you want, but it may be too advanced, have you studied the components of acceleration yet? (##a_c and a_t##)?