When and where will the collision occur in a one lane tunnel?

[steph35]

Finding a collision time...

Homework Statement

Sue, driving at 33 m/s enter a one lane tunnel. She then observes a slow moving van 175 m ahead traveling with velocity 5.40 m/s. Sue applies here brakes but can accelerate at only -2.00m/s^2.

Homework Equations

Determine how far into the tunnel and at what time the collision occurs.

The Attempt at a Solution

 

[Redbelly98]

Hello,

FYI, it's forum policy that you show the relevant equations and, more importantly, show your attempt at solving the problem, before you can get help with it.

See item #1 here:
https://www.physicsforums.com/showthread.php?t=94379

 

[baba89]

To find the collision time, we can use the equation:
t = (vf - vi)/a
Where:
t = time in seconds
vf = final velocity in m/s
vi = initial velocity in m/s
a = acceleration in m/s^2

In this scenario, Sue's initial velocity (vi) is 33 m/s and her final velocity (vf) is 0 m/s, since she is trying to come to a stop. The acceleration (a) is -2.00 m/s^2.
Plugging these values into the equation, we get:
t = (0 - 33)/(-2.00)
t = 16.5 seconds

This means that it will take Sue 16.5 seconds to come to a complete stop.
To find the distance traveled during this time, we can use the equation:
d = vi*t + (1/2)*a*t^2
Where:
d = distance in meters
vi = initial velocity in m/s
t = time in seconds
a = acceleration in m/s^2

Plugging in the values, we get:
d = (33*16.5) + (1/2)*(-2.00)*(16.5)^2
d = 544.5 meters

This means that Sue will have traveled 544.5 meters into the tunnel before coming to a stop.
To find the collision time, we can use the following equation:
t = d/vf
Where:
t = time in seconds
d = distance in meters
vf = final velocity in m/s

In this scenario, the distance (d) is 175 meters and the final velocity (vf) is 5.40 m/s.
Plugging in the values, we get:
t = 175/5.40
t = 32.41 seconds

This means that the collision will occur after 32.41 seconds, at a distance of 175 meters from the entrance of the tunnel.