You can use this 'suvat' equation of linear motion
[tex] s = ut + \frac{1}{2} a {t}^{2} [/tex]
From the question, the racer starts from rest so the initial velocity
[tex]u = 0 {ms}^{ - 1} [/tex]
The acceleration,
[tex]a= 14 {ms}^{ - 2} [/tex]
And distance
[tex]s = 424m[/tex]
We can substitute this values to find t
[tex] 424= (0)t + \frac{1}{2} (14) {t}^{2} [/tex]
[tex] 424= 7{t}^{2} [/tex]
Dividing by 7, we have
[tex] \frac{424}{7} = {t}^{2} [/tex]
[tex] \sqrt{ \frac{424}{7} } = t[/tex]
[tex]t = 7.8 \: s[/tex]
Therefore the race took 7.8 seconds
