College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Question
![**Physics Problem Example**
**Problem:**
A truck accelerates at a constant acceleration of 5.2 m/s² from rest. How far does the truck travel in the first 3.9 seconds, in meters?
**Solution:**
To determine the distance traveled by the truck, we can use the kinematic equation for distance under constant acceleration:
\[ d = v_i t + \frac{1}{2} a t^2 \]
Where:
- \( d \) = distance
- \( v_i \) = initial velocity (0 m/s in this case, as the truck starts from rest)
- \( t \) = time (3.9 seconds)
- \( a \) = acceleration (5.2 m/s²)
Since the truck starts from rest, the initial velocity \( v_i \) is 0. Thus, the equation simplifies to:
\[ d = \frac{1}{2} a t^2 \]
Plugging the given values into the equation:
\[ d = \frac{1}{2} \times 5.2 \, \text{m/s}^2 \times (3.9 \, \text{s})^2 \]
\[ d = 0.5 \times 5.2 \times 15.21 \]
\[ d = 2.6 \times 15.21 \]
\[ d \approx 39.55 \, \text{meters} \]
**Conclusion:**
The truck travels approximately 39.55 meters in the first 3.9 seconds.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8b894686-37de-488d-886f-184c412a3b38%2F68864949-ba80-4e4b-8575-5a8a15163bde%2F8coweza_processed.png&w=3840&q=75)
Transcribed Image Text:**Physics Problem Example**
**Problem:**
A truck accelerates at a constant acceleration of 5.2 m/s² from rest. How far does the truck travel in the first 3.9 seconds, in meters?
**Solution:**
To determine the distance traveled by the truck, we can use the kinematic equation for distance under constant acceleration:
\[ d = v_i t + \frac{1}{2} a t^2 \]
Where:
- \( d \) = distance
- \( v_i \) = initial velocity (0 m/s in this case, as the truck starts from rest)
- \( t \) = time (3.9 seconds)
- \( a \) = acceleration (5.2 m/s²)
Since the truck starts from rest, the initial velocity \( v_i \) is 0. Thus, the equation simplifies to:
\[ d = \frac{1}{2} a t^2 \]
Plugging the given values into the equation:
\[ d = \frac{1}{2} \times 5.2 \, \text{m/s}^2 \times (3.9 \, \text{s})^2 \]
\[ d = 0.5 \times 5.2 \times 15.21 \]
\[ d = 2.6 \times 15.21 \]
\[ d \approx 39.55 \, \text{meters} \]
**Conclusion:**
The truck travels approximately 39.55 meters in the first 3.9 seconds.
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