Question

1. a cars motion is shown in the table below. determine if the acceleration is positive or negative and if the object if speeding up or slowing down. time 2 sec 4 sec 6 sec 8 sec velocity -16 mph -12 mph -8 mph -4 mph positive acceleration; speeding up positive acceleration; slowing down negative acceleration; speeding up negative acceleration; slowing down

Explanation:

Step1: Recall acceleration - velocity relationship

Acceleration $a=\frac{\Delta v}{\Delta t}$. If velocity is increasing over time, acceleration is positive and object is speeding up. If velocity is decreasing over time, acceleration is negative and object is slowing down.

Step2: Analyze the table

As time ($t$) increases from 2 sec to 8 sec, velocity ($v$) changes from - 16 mph to - 4 mph. The magnitude of the negative - velocity is decreasing. Since the velocity is becoming less negative (i.e., increasing in value in the number - line sense), the acceleration is positive and the object is speeding up.

Answer:

positive acceleration; speeding up