Chapter 4: Q.76 (page 109)

A car starts from rest on a curve with a radius of $120 m$ and accelerates tangentially at $1.0 m / s^{2}$ . Through what angle will the car have traveled when the magnitude of its total acceleration is $2.0 m / s^{2}$ ?

Short Answer

Expert verified

$θ = 49.64 °$

Step by step solution

Given Information

We are given with:

$radius = r = 120 m tangential acceleration = a_{t} = 1 m / s^{2} total acceleration = a = 2 m / s^{2}$

Calculation

The car have traveled when the magnitude of its total acceleration is $a = 2 m / s^{2}$ .

As we know the formula for angle:

$θ = \frac{d}{r} d = distance r = radius$

For distance:

localid="1648908492211" $d = \frac{1}{2} a_{t} t^{2} t = \frac{v}{a_{t}} t = time to traveled the car v = velocity of car d = \frac{v^{2}}{2 a_{t}} a_{r} r = v^{2} d = \frac{a_{r} r}{2 a_{t}} a_{r} = radical acceleration$

By putting values of distance and radius in angle formula:

localid="1648098776664" $θ = \frac{a_{r} r}{2 a_{t} r} θ = \frac{a_{r}}{2 a_{t}} θ = \frac{1}{2} \sqrt{\frac{a^{2}}{{a_{t}}^{2}} - 1}$

Now putting the values in formula, the angle is:

$θ = \frac{1}{2} \sqrt{\frac{2^{2}}{1^{2}} - 1} θ = 0.866 rad$

Converting angle from radian to degree:

localid="1649071100890" $θ = 0.866 rad \times \frac{180 °}{π rad} θ = 49.64 °$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

A car starts from rest on a curve with a radius of $120 m$ and accelerates tangentially at $1.0 m / s^{2}$ . Through what angle will the car have traveled when the magnitude of its total acceleration is $2.0 m / s^{2}$ ?

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Turning Points in Physics

Fluids

Circular Motion and Gravitation

Physical Quantities And Units

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

A car starts from rest on a curve with a radius of 120mand accelerates tangentially at 1.0m/s2 . Through what angle will the car have traveled when the magnitude of its total acceleration is 2.0m/s2 ?

Short Answer

Step by step solution

Given Information

Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Waves Physics

Turning Points in Physics

Fluids

Circular Motion and Gravitation

Physical Quantities And Units

Geometrical and Physical Optics

Study anywhere. Anytime. Across all devices.

A car starts from rest on a curve with a radius of $120 m$ and accelerates tangentially at $1.0 m / s^{2}$ . Through what angle will the car have traveled when the magnitude of its total acceleration is $2.0 m / s^{2}$ ?