show me the steps , i want to understand it ### Particle Motion AnalysisWe are given a specific acceleration function and initial velocity for a particle moving in a linear path. The parameters are as follows:- **Acceleration function** \( a(t) \) in \( \text{m/s}^2 \): \( a(t) = 2t + 4 \)- **Initial velocity** \( v(0) \) in \( \text{m/s} \): \( v(0) = -5 \)- **Time interval**: \( 0 \leq t \leq 3 \)### Tasks for Solution#### (a) Finding the VelocityWe need to determine the velocity \( v(t) \) of the particle as a function of time \( t \). \[ v(t) = \boxed{\text{Solution (m/s)}} \]#### (b) Finding the Distance TraveledWe need to calculate the total distance the particle travels within the given time interval \( 0 \leq t \leq 3 \).\[ \boxed{\text{Distance (m)}} \]### Explanation of the Given Diagram- The diagram includes the acceleration formula and the initial conditions for the velocity.- Two blank boxes are provided for inputting the solutions (one for velocity, one for distance traveled).To fill the blanks:1. Integrate the acceleration function \( a(t) \) to find the velocity function \( v(t) \).2. Use the velocity function to calculate the distance traveled over the given interval.

The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle moving along a line. a(t) = 2t + 4, v(0) = -5, 0 sts3 (a) Find the velocity (in m/s) at time t. v(t) = m/s (b) Find the distance traveled (in m) during the given time interval.

The acceleration function (in m/s2) and the initial velocity v(0) (in m/s) are given for a particle moving along a line. a(t) = 2t + 4, v(0) = -5, 0 sts3 (a) Find the velocity (in m/s) at time t. v(t) = m/s (b) Find the distance traveled (in m) during the given time interval.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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