Answer:
Step-by-step explanation:
Average speed is the change in distance of a body with respect to time. This is expressed as:
[tex]v = \delta y/\delta t\\v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}[/tex]
Given the function of the height in metres expressed as y = 56t − 1.86t² and time interval [1,2]
t₁ = 1sec and t₂ = 2 secs
y(t₂) = 56t₂ − 1.86t₂²
y(2) = 56(2) − 1.86(2)²
y(2) = 112-7.44
y(2) = 104.56
y(t₁ ) = 56t₁ − 1.86t₁ ²
y(1) = 56(1) − 1.86(1)²
y(1) = 56-1.86
y(1) = 54.14
Substituting the derived value into the formula for finding the average speed:
[tex]v = \dfrac{y(t_2)-y(t_1)}{t_2-t_1}\\\\v = \dfrac{104.56-54.14}{2-1}\\\\v = \dfrac{50.42}{1}\\\\v = 50.42m/s[/tex]
Hence, the average speed over the given time intervals. [1, 2] is 50.42m/s
