Question

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

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:

\(14.4\)