   Chapter 2, Problem 58AP

Chapter
Section
Textbook Problem

A speedboat moving at 30.0 m/s approaches a no-wake buoy marker 1.00 × 102 m ahead. The pilot slows the boat with a constant acceleration of −3.50 m/s2 by reducing the throttle. (a) How long does it take the boat to reach the buoy? (b) What is the velocity of the boat when it reaches the buoy?

(a)

To determine
The time taken for the boat to reach the buoy.

Explanation

Given Info:

The initial velocity of the boat is 30.0m/s .

The acceleration of the boat is 3.50m/s2 .

The displacement of the boat is 100m .

The formula used to calculate the displacement of the boat is,

Δx=v0t+12at2

• Δx is the displacement of the boat
• t is time took by the boat to reach the buoy
• v0 is the initial velocity of the boat
• a is the acceleration

Substitute 30.0m/s for v0 , 3.50m/s2 for a and 100m for Δx to find t .

(100m)=(30.0m/s)t+12(3

(b)

To determine
The velocity of the boat when it reaches the buoy.

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