Question

The table shows the height of a soccer ball that has been kicked from the ground over time. (For reference: h(t) = 144 – 16t2) Time (seconds) Height (feet) 0 0 0.5 16 1 24 1.25 25 1.5 24 2 16 2.5 0 Which statement describes the rate of change of the height of the ball over time? The rate of change is not constant and decreases over the entire time. Between 0 and 0.5 second the ball rises 16 feet, but between 0.5 and 1 second it rises only 8 more feet. The rate of change is not constant and increases over the entire time. Between 1.5 and 2 seconds the ball falls 8 feet, but between 2 and 12.5 seconds it falls 16 more feet. The rate of change is not constant and decreases then increases over time. The ball rises by 16 in the first half second, but only 8 feet over the next one. After it reaches 25 feet in the air, the ball drops. The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Answer 1

Answer : option D

The rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.

Rate of change is nothing but the slope

To find slope we use formula $\frac{Change in height }{change in time}$

Time (seconds) Height (feet) Rate of change

0 -------------------------0

0.5 -----------------------16 --------------------$\frac{16-0}{0.5-0} =32$

1 ----------------------24 --------------------$\frac{24-16}{1-0.5} =16$

1.25 -----------------------25--------------------$\frac{25-24}{1.25-1} =4$

1.5 -------------------------24 --------------------$\frac{24-25}{1.5-1.25} =-4$

2 ----------------------------16 --------------------$\frac{16-24}{2-1.5} =-16$

2.5 -------------------------0 --------------------$\frac{0-16}{2.5-2} =-32$

Rate of change is positive till 1.25 seconds and then it becomes negative. From this it is clear that, the rate of change is not constant and increases then decreases over time. The height of the ball above ground gets larger until 1.25 seconds and then gets smaller after that time.