Final answer:
It is true that an object traveling in the positive direction and accelerating in the negative direction will slow down. This is due to acceleration being defined as the rate of change of velocity, and having acceleration in the opposite direction of the velocity will reduce the object's speed.
Step-by-step explanation:
The statement is true: if an object is traveling in the positive direction (meaning its velocity vector is pointed in the direction defined as positive) and it is experiencing an acceleration in the negative direction (meaning the acceleration vector is pointed in the opposite direction of the positive direction), then indeed the object will slow down. This is because acceleration defines the rate of change of velocity over time, and when an object's acceleration is opposite to its direction of velocity, the speed of the object decreases.
For example, if a car is moving to the right (positive direction) and its wheels are producing an acceleration to the left (negative direction), this would result in a decrease in the car's speed to the right, hence slowing the car down. This is sometimes referred to as deceleration or negative acceleration.
Concerning the true/false statements, the position vs time graph of an object that is speeding up will not be a straight line; it will be curved, indicating a change in velocity, so the answer is false. The vector for a negative acceleration does indeed point in the opposite direction of a positive acceleration vector, making that statement true. Lastly, a plot of displacement versus time for an object with constant acceleration will be curved, and the plot of displacement versus time squared will indeed be a straight line, so the answer is true.