The speed of an object is the rate of distance over time. The value of time (t) at the greatest speed of the ball is at 2 seconds
First, we calculate the speed using:
[tex]Speed = \frac{h(t)}{t}[/tex] --- i.e. distance/time
At t = 0, h(t) = 5
So;
[tex]Speed = \frac{5}{0} = unde fine d[/tex]
At t = 3, h(t) = 12
[tex]Speed = \frac{12}{3} = 4[/tex]
At t = 6, h(t) = 15
[tex]Speed = \frac{15}{6} = 2.5[/tex]
At t = 9, h(t) = 11
[tex]Speed = \frac{11}{9} = 1.2[/tex]
At t = 12, h(t) = 6
[tex]Speed = \frac{6}{12} = 0.5[/tex]
At t = 15, h(t) = 0
[tex]Speed = \frac{0}{15} = 0[/tex]
By comparing the above values, we notice that as time and height increases, the value of speed reduces.
This means that the greatest value of speed will be at the least value of time (t).
From the given options, the least value of time is at:
[tex]t = 2[/tex]
Hence, the value of time (t) at the greatest speed of the ball is at 2 seconds
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