The velocity (in feet/second) of a maglev is v(t)=0.2 t+3 (0 ≤t ≤120) At t=0, it is at the sta

Name: Problem 66, Chapter 11: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-10T15:49:10-08:00
Duration: 1 min 33 s
Channel: Gregory Higby
Description: The velocity (in feet/second) of a maglev is v(t)=0.2 t+3 (0 ≤t ≤120) At t=0, it is at the station. Find the function giving the position of the maglev at time t, assuming that the motion takes place along a straight stretch of track.

step 1 When they give you a velocity problem, and we have 0 .2t plus 3, the key to finding its position

Question

The velocity (in feet/second) of a maglev is $$ v(t)=0.2 t+3 \quad(0 \leq t \leq 120) $$ At $t=0$, it is at the station. Find the function giving the position of the maglev at time $t$, assuming that the motion takes place along a straight stretch of track.

   The velocity (in feet/second) of a maglev is
$$
v(t)=0.2 t+3 \quad(0 \leq t \leq 120)
$$
At $t=0$, it is at the station. Find the function giving the position of the maglev at time $t$, assuming that the motion takes place along a straight stretch of track.

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 11, Problem 66

Instant Answer

Solved by Expert Gregory Higby

05/10/2021

Step 1

2t + 3, and we need to find the position function, s(t). Show more…

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The velocity (in feet/second) of a maglev is $$ v(t)=0.2 t+3 \quad(0 \leq t \leq 120) $$ At $t=0$, it is at the station. Find the function giving the position of the maglev at time $t$, assuming that the motion takes place along a straight stretch of track.

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Key Concepts

Kinematics of Linear Motion

Kinematics in one dimension relates position, velocity, and acceleration. Specifically, the velocity function is the time derivative of the position function, and integrating velocity yields the position function along a straight path.

Integration

Integration is the process of finding an antiderivative, which is essential in recovering a function from its rate of change. In motion problems, integrating the velocity function with respect to time provides the position function.

Initial Condition

An initial condition specifies the starting state of a system, such as the initial position in kinematics. It is used to determine the constant of integration after finding the general antiderivative.

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