Final answer:
A car speeding up in the backward direction, designated as negative, would have a negative change in velocity and negative acceleration, as the increase in speed and acceleration are in the same negative direction.
Step-by-step explanation:
When a car is speeding up in the backward direction and we designate the backward direction as negative (-), the change in velocity is also negative. This is because if the car is initially moving backward at a certain speed (say, -10 m/s) and then speeds up in that same backward direction to a higher speed (say, -15 m/s), the change in velocity would be the final velocity minus the initial velocity, which in this case is (-15 m/s) - (-10 m/s), resulting in -5 m/s. Since the number is negative, it indicates that the change in velocity is also negative. Moreover, because the car's acceleration is in the same direction as its increase in speed, its acceleration would also be negative according to the assigned coordinate system.