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Answer :
Answer:4.39 s
Explanation:
Given
initial velocity [tex]u=0[/tex]
acceleration [tex]a=12.8 m/s^2[/tex]
velocity acquired by sled in [tex]t_1[/tex] time
[tex]v=0+at[/tex]
[tex]v=12.8t_1[/tex]
distance traveled by sled in [tex]t_1 s[/tex]
[tex]v^2-u^2=2as[/tex]
[tex](12.8t_1)^2-0=2\times 12.8\times s_1[/tex]
[tex]s_1=6.4\cdot t_1^2[/tex]
distance traveled in [tex]t_2[/tex] time with velocity [tex]v=12.8t_1[/tex]
[tex]s_2=v\times t_2[/tex]
[tex]s_2=12.8\times t_1\times t_2[/tex]
[tex]s_2=12.8\cdot t_1\cdot t_2[/tex]
[tex]s_1+s_2=5.37\times 10^3[/tex]
[tex]6.4t_1^2+12.8t_1t_2=5370[/tex]----1
[tex]t_1+t_2=97.7 s[/tex]
[tex]t_2=97.7-t_1[/tex]
substitute the value of [tex]t_2[/tex] in 1
we get
[tex]6.4t_1^2-1250.56t_1+5370=0[/tex]
thus [tex]t_1=\frac{1250.56-1194.33}{12.8}=4.39 s[/tex]
[tex]t_1=4.39 s[/tex]
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Rewritten by : Jeany
