Answer:
[tex]t=16.67s[/tex]
Explanation:
From the question, acceleration from [tex]6m/s^2 \ to \ 0m/s^2[/tex] in 10 seconds.
Acceleration function can be written as:-
[tex]a_t=6-0.6t[/tex]
From the acceleration equation, we can obtain the velocity equation:
[tex]v(t)=\int\limits^t_b {0} \, dv=\int\limits^t_0 {a(t)} \, dt\\v(t)=\int\limits^t_0 {(6-06t)} \, dt=6t-0.3t^2\\*dv=a(t)dt[/tex]
We calculate velocity after 10sec from the above v(t) as [tex]30m/s[/tex].
To obtain distance travelled after 10 seconds:-
[tex]S=\int\limits^{10}_0 {6t-0.3t^2} \, dt=|3t^2-0.1t^3| \ *lims(10,0)\\ S=200m[/tex]
Therefore 200m is for 10seconds, and next 200m at 30m/s
Total time=[tex]10+\frac{200}{30}=16.67s[/tex]
