Answer:
8.94 seconds
Explanation:
t = Time taken
u = Initial velocity
v = Final velocity
s = Displacement
a = Acceleration
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s_1=0t+\frac{1}{2}\times 0.6\times t^2\\\Rightarrow s_1=0.3t^2[/tex]
[tex]s=ut+\frac{1}{2}at^2\\\Rightarrow s_2=0t+\frac{1}{2}\times 0.45\times t^2\\\Rightarrow s_2=0.225t^2[/tex]
They both will run for the same amount of time assuming that they started running at the same time and together they will travel 42 m.
[tex]42=0.3t^2+0.225t^2\\\Rightarrow t=\sqrt{\frac{42}{0.3+0.225}}\\\Rightarrow t=8.94\ s[/tex]
The time at which they will collide is 8.94 seconds
