Respuesta :
Answer:
One must wait 0.88 secs before starting the red car
Explanation:
To calculate how much time to wait before starting the red car from rest, we will calculate the time it will take the blue car to reach the end of the track from rest and the time it will take the red car to reach the end of the track from rest; then, the difference between these times is the time one must wait before starting the red car from rest such that two cars reach the end of the track at the same time
For the red car,
Acceleration = 4.00 m/s²
Initial velocity = 0 m/s (Since it is starting from rest)
Distance = 9.00 m
Let the time spent by the red car be [tex]t_{r}[/tex]
From one of the equations of kinematics for linear motion
[tex]S = ut + \frac{1}{2}at^{2}[/tex]
Where
[tex]S[/tex] is the distance traveled
[tex]u[/tex] is the initial velocity
[tex]t[/tex] is the time
and [tex]a[/tex] is the acceleration
Then, for the red car
[tex]9.00 = (0)(t_{r}) + \frac{1}{2}(4.00)(t_{r})^{2}[/tex]
[tex]9.00 = (2.00)(t_{r})^{2}[/tex]
[tex]t_{r} = \sqrt{\frac{9.00}{2.00} }[/tex]
[tex]t_{r} =2.12 secs[/tex]
This is the time it will take the red car to reach the end of the track
For the blue car
Acceleration = 2.00 m/s²
Initial velocity = 0 m/s (Since it is starting from rest)
Distance = 9.00 m
Let the time spent by the red car be [tex]t_{b}[/tex]
Also from
[tex]S = ut + \frac{1}{2}at^{2}[/tex]
[tex]9.00 = (0)(t_{r}) + \frac{1}{2}(2.00)(t_{b})^{2}[/tex]
[tex]9.00 = (t_{b})^{2}[/tex]
[tex]t_{b} = \sqrt{9}[/tex]
[tex]t_{b} = 3secs[/tex]
This is the time it will take the blue car to reach the end of the track
The difference of the times is
[tex]t_{b} - t_{r}[/tex] = 3 secs - 2.12 secs
= 0.88 secs
Hence, one must wait 0.88 secs before starting the red car
