Speedy Sue, driving at 35.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 160 m ahead traveling at 5.20 m/s. Sue applies her brakes but can accelerate only at −1.90 m/s2 because the road is wet. Will there be a collision?

Hence, there will be a collision

Explanation:

First we calculate total distance covered by the speedy sue's car before coming to rest:

2as = Vf² - Vi²

where,

a = deceleration = - 1.9 m/s²

s = distance covered = ?

Vf = Final Velocity = 0 m/s (since car finally stops)

Vi = Initial Velocity = 35 m/s

Therefore,

2(-1.9 m/s²)s = (0 m/s)² - (35 m/s)²

s = 322.37 m

Now, we calculate time taken by car to stop:

Vf = Vi + at

0 m/s = 35 m/s + (-1.9 m/s²)t

t =  18.42 s

Now, we calculate distance traveled by van in this time:

s₁ = V₁t

where,

s₁ = distance traveled by van = ?

V₁ = speed of van = 5.2 m/s

Therefore,

s₁ = (5.2 m/s)(18.42 s)

s₁ = 95.78 m

Now, for collision to occur, the following relation must be satisfied:

s ≥ 160 m + s₁

using values:

322.37 m > 160 m + 95.78 m

322.37 m > 255.78 m

Hence, there will be a collision

the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.

true tan speed = ang vel x radius