Help me find the displacement at time T and the total distance traveled, thank you! Suppose that a particle moves along a straight line with velocity v(t) = 8 - 3t, where 0 ≤ t ≤ 1 (inmeters per second). Find the formula for the displacement of the particle and the total distance it hastraveled at time t = 1 seconds.Displacement at time t is:Total distance traveled:Submit Questionmeters in 1 seconds

Given: A particle moves along a straight line with velocity where .To find the formula for the…

Answered: Suppose that a particle moves along a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter2: Equations And Inequalities

Section2.7: More On Inequalities

Problem 44E

See similar textbooks

Related questions

Question

Help me find the displacement at time T and the total distance traveled, thank you!

Suppose that a particle moves along a straight line with velocity v(t) = 8 - 3t, where 0 ≤ t ≤ 1 (in
meters per second). Find the formula for the displacement of the particle and the total distance it has
traveled at time t = 1 seconds.
Displacement at time t is:
Total distance traveled:
Submit Question
meters in 1 seconds

Expert Solution

Step 1: Introduction:

Given: A particle moves along a straight line with velocity $v left parenthesis t right parenthesis equals 8 minus 3 t$ where $0 less or equal than t less or equal than 1$ .

To find the formula for the displacement of the particle and the total distance it has travelled at time $t equals 1 space s e c o n d s$ .

Concepts used:

Given the velocity function $v left parenthesis t right parenthesis$ the displacement function $s left parenthesis t right parenthesis$ is given by $s left parenthesis t right parenthesis equals integral subscript 0 superscript t v left parenthesis u right parenthesis d u$ .

Integration formula: $integral left parenthesis f left parenthesis x right parenthesis plus g left parenthesis x right parenthesis right parenthesis d x equals integral f left parenthesis x right parenthesis d x plus integral g left parenthesis x right parenthesis d x$ .

$integral c f left parenthesis x right parenthesis d x equals c integral f left parenthesis x right parenthesis d x$ where $c$ is a constant.

$integral x to the power of n equals fraction numerator x to the power of n plus 1 end exponent over denominator n plus 1 end fraction plus C$ where $C$ is the constant of integration.

Distance is the total path covered by an object in motion in any direction. Displacement is the total change in position of an object along with the direction of motion. If the object is moving in a straight line distance and displacement are the same.