Starting from rest, an automobile's velocity v (in ft / sec ) is given by v=(180 t)/(2 t+10), wh

Name: Problem 106, Chapter 1: College Algebra Essentials
Uploaded: 2023-08-25T03:51:34-08:00
Duration: 1 min 23 s
Channel: Breanna Ollech
Description: Starting from rest, an automobile's velocity v (in ft / sec ) is given by v=(180 t)/(2 t+10), where t is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of 60 ft / sec (≈41 mph).

step 1 For this problem, we're given our equation for our velocity and we want to know the time when ou

Question

Starting from rest, an automobile's velocity $v$ (in $\mathrm{ft} / \mathrm{sec}$ ) is given by $v=\frac{180 t}{2 t+10},$ where $t$ is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of $60 \mathrm{ft} / \mathrm{sec}$ $(\approx 41 \mathrm{mph})$.

   Starting from rest, an automobile's velocity $v$ (in $\mathrm{ft} / \mathrm{sec}$ ) is given by $v=\frac{180 t}{2 t+10},$ where $t$ is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of $60 \mathrm{ft} / \mathrm{sec}$ $(\approx 41 \mathrm{mph})$.

College Algebra Essentials

Julie Miller 1st Edition

Chapter 1, Problem 106

Instant Answer

Solved by Expert Breanna Ollech

08/25/2023

Step 1

So, we set $v$ equal to 60 and solve for $t$: \[60 = \frac{180 t}{2 t+10}\] Show more…

Show all steps

Thanks for your feedback!

Starting from rest, an automobile's velocity $v$ (in $\mathrm{ft} / \mathrm{sec}$ ) is given by $v=\frac{180 t}{2 t+10},$ where $t$ is the time in seconds after the car begins forward motion. Determine the time required for the car to reach a speed of $60 \mathrm{ft} / \mathrm{sec}$ $(\approx 41 \mathrm{mph})$.

Play audio

Feedback

Breanna Ollech and 60 other subject Algebra educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Rational Equations

Rational equations contain variables in the numerator or denominator of fractions. Solving these equations often requires techniques like cross-multiplication to eliminate the fractions and isolate the variable of interest.

Kinematics

Kinematics involves analyzing the motion of objects without considering the forces causing the motion. In problems like this one, the relationship between velocity and time is examined, and mathematical functions are used to model how velocity changes over time.

Algebraic Manipulation

Algebraic manipulation refers to the process of rearranging equations using basic algebraic operations. This includes isolating variables, combining like terms, and using inverse operations, all of which are essential steps when solving for time in the context of a given velocity function.

Please give Ace some feedback