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At time t≥ 0, the velocity of a body moving along the horizontal s-axis is v= t² - 4t + 3. (a) Find the body's acceleration each time the velocity is zero. (b) When is the body moving forward? Backward? (c) When is the body's velocity increasing? Decreasing?

At time t≥ 0, the velocity of a body moving along the horizontal s-axis is v= t² - 4t + 3. (a) Find the body's acceleration each time the velocity is zero. (b) When is the body moving forward? Backward? (c) When is the body's velocity increasing? Decreasing?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Physics Problem: Motion Along a Horizontal Axis** At time \( t \ge 0 \), the velocity of a body moving along the horizontal \( s \)-axis is given by \( v = t^2 - 4t + 3 \). **Questions:** (a) Find the body's acceleration each time the velocity is zero. (b) When is the body moving forward? When is it moving backward? (c) When is the body's velocity increasing? When is it decreasing? **Detailed Explanation:** 1. **Finding the acceleration when velocity is zero:** To solve this, we need to find the instances when the velocity \( v \) is zero, and then find the acceleration at those points. 2. **Determining when the body is moving forward and backward:** Analyze the intervals of time \( t \) where the velocity function \( v(t) = t^2 - 4t + 3 \) is positive (for forward motion) and negative (for backward motion). 3. **Determining the increasing and decreasing velocity:** This involves finding the acceleration \( a(t) \) and analyzing when \( a(t) \) is positive (indicating increasing velocity) and negative (indicating decreasing velocity). **Note:** Remember to perform necessary differentiation to find the acceleration \( a(t) \).
Transcribed Image Text:**Physics Problem: Motion Along a Horizontal Axis** At time \( t \ge 0 \), the velocity of a body moving along the horizontal \( s \)-axis is given by \( v = t^2 - 4t + 3 \). **Questions:** (a) Find the body's acceleration each time the velocity is zero. (b) When is the body moving forward? When is it moving backward? (c) When is the body's velocity increasing? When is it decreasing? **Detailed Explanation:** 1. **Finding the acceleration when velocity is zero:** To solve this, we need to find the instances when the velocity \( v \) is zero, and then find the acceleration at those points. 2. **Determining when the body is moving forward and backward:** Analyze the intervals of time \( t \) where the velocity function \( v(t) = t^2 - 4t + 3 \) is positive (for forward motion) and negative (for backward motion). 3. **Determining the increasing and decreasing velocity:** This involves finding the acceleration \( a(t) \) and analyzing when \( a(t) \) is positive (indicating increasing velocity) and negative (indicating decreasing velocity). **Note:** Remember to perform necessary differentiation to find the acceleration \( a(t) \).
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