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

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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

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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

Radiation

Force

Circular Motion and Gravitation

Space Physics

Magnetism and Electromagnetic Induction

Physical Quantities And Units

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 $2.0 m / s^{2}$ ?