Answer:
The collision will occur 7.12 s from the moment Sue sees the van.
The collision will occur 196.9 m inside the tunnel.
Explanation:
The equation for the position of an object moving in a straight line is the following:
x = x0 + v0 · t + 1/2 · a · t²
Where
x = position at time t
x0 = initial position
t = time
v0 = initial velocity
a = acceleration
If the object moves with constant speed, then a = 0 and x = x0 + v · t
If there is a collision, there will be a time "t" at which the position of Sue and the van is the same.
Let´s place the center of the frame of reference at the position of Sue when she sees the van and applies the brakes.
x Sue = x van
x0 + v0 · t + 1/2 · a · t² = x0 + v · t (x0 Sue = 0, x0 van = 160 m)
33 m/s · t - 1/2 · 1.50 m/s² · t² = 160m + 5.20 m/s · t
33 m/s · t - 0.75 m/s² · t² = 160m + 5.20 m/s · t
- 0.75 m/s² · t² + 27.8 m/s · t -160 m = 0
t = 7.12 s ( the other value is t = 29.9, we take the lower one because the collision will occur only once).
The collision will occur 7.12 s from the moment Sue sees the van.
The distance traveled during that time will be:
x = x0 + v0 · t + 1/2 · a · t²
x = 33 m/s · 7.12 s - 1/2 · 1.50 m/s² · (7.12 s)²
x = 196.9 m
The collision will occur 196.9 m inside the tunnel.
