Chapter 8: Q.28 (page 199)

A new car is tested on a $200 - m$ -diameter track. If the car speeds up at a steady $1.5 m / s^{2}$ , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Short Answer

Expert verified

The magnitude of its centripetal acceleration equal to the tangential acceleration after $8.2 s$ .

Step by step solution

Given Information

Diameter of the track : $d = 200 m$ .

Acceleration of the car $a_{t} = 1.5 m / s^{2}$ .

Explanation

According to the information:

$d -$ The diameter of the truck $= 200 m$

$a_{t} -$ Tangential acceleration $= 1.5 m / s^{2}$

The centripetal acceleration $a_{c}$ is given as follow:

$a_{c} = \frac{v^{2}}{r}$

Where,

$v -$ The velocity of the car

$r -$ The radius of the track

$t -$ The time

Applying the equation to find time

Centripetal acceleration $a_{c}$ $=$ Tangential acceleration $a_{t}$

$a_{t} = \frac{v^{2}}{r}$

$v = \sqrt{a_{t} \times r}$ (1)

The initial velocity of the car is zero.

Therefore, the tangential acceleration is given by kinematic equation as follow:

$v = a_{t} \times t$ (2)

From equation 1 and 2, we get

$\sqrt{a_{t} \times r} = a_{t} \times t$

$t = \sqrt{\frac{r}{a_{t}}}$

$t = \sqrt{\frac{d}{2 a_{t}}}$

$t = \sqrt{\frac{200}{2 \times 1.5}}$

$t = \sqrt{66.67}$

$t = 8.2 s$

Final Answer

The magnitude of its centripetal acceleration equal to the tangential acceleration after $8.2 s$ .

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A new car is tested on a $200 - m$ -diameter track. If the car speeds up at a steady $1.5 m / s^{2}$ , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Short Answer

Step by step solution

Given Information

Explanation

Applying the equation to find time

Final Answer

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A new car is tested on a 200-m-diameter track. If the car speeds up at a steady 1.5m/s2 , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?

Short Answer

Step by step solution

Given Information

Explanation

Applying the equation to find time

Final Answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Magnetism

Fields in Physics

Engineering Physics

Solid State Physics

Radiation

Oscillations

Study anywhere. Anytime. Across all devices.

A new car is tested on a $200 - m$ -diameter track. If the car speeds up at a steady $1.5 m / s^{2}$ , how long after starting is the magnitude of its centripetal acceleration equal to the tangential acceleration?