The distance of the track is 600 m
Explanation:
The two cars move by uniformly accelerated motion, so we the distance they cover after a time t is described by the following suvat equation
[tex]d=ut+\frac{1}{2}at^2[/tex]
where
u is the initial velocity
a is the acceleration
For car 1, we have
[tex]d_1 = u_1 t + \frac{1}{2}a_1 t^2[/tex]
where
[tex]u_1 = 7 m/s[/tex] is the initial velocity of car 1
[tex]a_1 = 0.4 m/s^2[/tex] is the acceleration of car 1
So the equation can be rewritten as
[tex]d_1 = 7t + 0.2t^2[/tex]
For car 2, we have
[tex]d_2 = u_2 t + \frac{1}{2}a_2 t^2[/tex]
where
[tex]u_2 = 4 m/s[/tex] is the initial velocity of car 2
[tex]a_2 = 0.5 m/s^2[/tex] is the acceleration of car 2
So the equation can be rewritten as
[tex]d_2= 5t + 0.25t^2[/tex]
The two cars finish the race at the same time: this means that they cover the same distance in the same time t, so we can write
[tex]d_1 = d_2\\7t + 0.2t^2=5t + 0.25t^2[/tex]
And solving for t, we find
[tex]2t - 0.05t^2= 0\\t(2-0.05t)=0[/tex]
Which gives two solutions:
t = 0 (initial instant)
t = 40 s
Therefore, the distance of the track is
[tex]d_1 = 7t +0.2t^2 = 7\cdot 40+0.2\cdot 40^2=600 m[/tex]
Learn more about accelerated motion:
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