a scientist drops a ball off the edge of a platform on mars. the distance, d(t). in meters, the ball travels…

a scientist drops a ball off the edge of a platform on mars. the distance, d(t). in meters, the ball travels after t seconds can be modeled by the function d(t) = 1.2t². what is the average speed, in meters per second, of the ball between 4 and 8 seconds after it was dropped? meters per second

a scientist drops a ball off the edge of a platform on mars. the distance, d(t). in meters, the ball travels after t seconds can be modeled by the function d(t) = 1.2t². what is the average speed, in meters per second, of the ball between 4 and 8 seconds after it was dropped? meters per second

Answer

Explanation:

Step1: Find the distance at (t = 4) and (t = 8)

The formula for average speed is (\text{Average Speed}=\frac{d(t_2)-d(t_1)}{t_2 - t_1}). Given (d(t)=1.2t^{2}). When (t = 4), (d(4)=1.2\times4^{2}=1.2\times16 = 19.2) meters. When (t = 8), (d(8)=1.2\times8^{2}=1.2\times64 = 76.8) meters.

Step2: Calculate the average speed

Here (t_1 = 4), (t_2=8), (d(t_1)=19.2), (d(t_2)=76.8). (\text{Average Speed}=\frac{d(8)-d(4)}{8 - 4}=\frac{76.8-19.2}{4}). (\frac{76.8 - 19.2}{4}=\frac{57.6}{4}=14.4)

Answer:

(14.4)