   Chapter 2, Problem 35P

Chapter
Section
Textbook Problem

Speedy Sue, driving at 30.0 m/s, enters a one-lane tunnel. She then observes a slow-moving van 155 m ahead traveling at 5.00 m/s. Sue applies her brakes but can accelerate only at −2.00 m/s2 because the road is wet. Will there be a collision? State how you decide. If yes, determine how far into the tunnel and at what time the collision occurs. If no, determine the distance of closest approach between Sue’s car and the van.

To determine
If the collision occurs or not.

Explanation

Given Info:

The initial velocity of Sue’s car is 30.0m/s

The acceleration of Sue’s car is 2.00m/s2

The initial velocity of van is 5.00m/s

The acceleration of van is 0

The initial position of the van is 155m

The formula used to calculate the final position of  Sue’s car is,

xS=v0St+12aSt2

• xS is the final position of Sue’s car
• v0 is the initial velocity of Sue’s car
• a is the acceleration of Sue’s car
• t is the time

Substitute 30.0m/s for v0S and 2.00m/s2 for a to find xS . xS=(30.0m/s)t+12(2.00m/s2)t2=(30.0m/s)t+(1.00m/s)t+12(0)t2=(30.0m/s)t+(1.00m/s)t2 I

The formula used to calculate the final position of the van is,

xv=x0v+v0vt+12avt2

• xv is the final position of van
• v0v is the initial velocity of  the van
• a is the acceleration of the van
• x0v is the initial position of the van
• t is the time

Substitute 5

To determine
The distance at which collision occurs.

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