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Answer:
[tex]D_T=18.567m[/tex]
Explanation:
From the question we are told that:
Acceleration [tex]a=8.0 m/s^2[/tex]
Displacement [tex]d=1.05 m[/tex]
Initial time [tex]t_1=6.0s[/tex]
Final Time [tex]t_2=2.5s[/tex]
Generally the equation for Velocity of 1.05 travel is mathematically given by
Using Newton's Law of Motion
[tex]V^2=2as[/tex]
[tex]V=\sqrt{2*6*1.05}[/tex]
[tex]V=4.1m/s[/tex]
Generally the equation for Distance traveled before stop is mathematically given by
[tex]d_2=v*t_1[/tex]
[tex]d_2=3.098*4[/tex]
[tex]d_2=12.392[/tex]
Generally the equation for Distance to stop is mathematically given by
Since For this Final section
Final velocity [tex]v_3=0 m/s[/tex]
Initial velocity [tex]u_3=4.1 m/s[/tex]
Therefore
Using Newton's Law of Motion
[tex]-a_3=(4.1)/(2.5)[/tex]
[tex]-a_3=1.64m/s^2[/tex]
Giving
[tex]v_3^2=u^2-2ad_3[/tex]
Therefore
[tex]d_3=\frac{u_3^2}{2ad_3}[/tex]
[tex]d_3=\frac{4.1^2}{2*1.64}[/tex]
[tex]d_3=5.125m[/tex]
Generally the Total Distance Traveled is mathematically given by
[tex]D_T=d_1+d_2+d_3[/tex]
[tex]D_T=5.125m+12.392+1.05 m[/tex]
[tex]D_T=18.567m[/tex]