Q38P At times=,t1=12s, a car is locat... [FREE SOLUTION]

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Chapter 1: Q38P (page 40)

At times=, $t_{1} = 12$ s, a car is located at $< 84, 78, 24 >$ m and has velocity $< 4, 0, - 3 >$ m/s. At time $t_{2} = 18$ s, what is the position of the car? (The velocity is constant in magnitude and direction during this time interval.)

Short Answer

Expert verified

The position of the car is: ${\overset{鈬赌}{r}}_{2} = <108, 78, 6>$ m.

Step by step solution

Identification of given data

Location at times, $12 s, {\overset{鈬赌}{r}}_{1} = <84, 78, 24> m$

Velocity at time s, $12 s, \overset{鈬赌}{v} 1 = <4, 0, - 3>$ =m/s

$t_{1} = 12 s t_{2} = 18 s$

Calculating position of the car

A position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents the position of a point P in space in relation to an arbitrary reference originO.

To find the final position, use the following formula

This is valid because the velocity is constant and there is no acceleration.

Therefore,

$\overset{鈫�}{v} = \frac{鈭� \overset{鈫�}{r}}{鈭� t} 鈬� 鈭� \overset{鈫�}{r} = \overset{鈫�}{v} 鈭� t 鈬� \overset{鈫�}{r_{2}} = \overset{鈫�}{r_{1}} + \overset{鈫�}{v} (t_{2} - t_{1})$

This is valid because the velocity is constant and there is no acceleration.

Therefore,

$\overset{鈫�}{r_{2}} = <84, 78, 24> + <4, 0, - 3> <8 - 12> \overset{鈫�}{r_{2}} = <84, 78, 24> + <24, 0, - 18> \overset{鈫�}{r_{2}} = <108, 78, 6> m$

Thus, the position of the car is $\overset{鈫�}{r_{2}} = <108, 78, 6> m$ .

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Location	t(s)	Position ( m)
A	0.0	(0,0,0)
B	1.0	(22.3,26.1,0)
C	2.0	(40.1,38.1,0)

91影视

At times=, $t_{1} = 12$ s, a car is located at $< 84, 78, 24 >$ m and has velocity $< 4, 0, - 3 >$ m/s. At time $t_{2} = 18$ s, what is the position of the car? (The velocity is constant in magnitude and direction during this time interval.)

Short Answer

Step by step solution

Identification of given data

Calculating position of the car

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91影视

At times=,t1=12s, a car is located at<84,78,24> m and has velocity<4,0,-3>m/s. At timet2=18s, what is the position of the car? (The velocity is constant in magnitude and direction during this time interval.)

Short Answer

Step by step solution

Identification of given data

Calculating position of the car

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Circular Motion and Gravitation

Oscillations

Conservation of Energy and Momentum

Force

Electricity and Magnetism

Thermodynamics

Study anywhere. Anytime. Across all devices.

At times=, $t_{1} = 12$ s, a car is located at $< 84, 78, 24 >$ m and has velocity $< 4, 0, - 3 >$ m/s. At time $t_{2} = 18$ s, what is the position of the car? (The velocity is constant in magnitude and direction during this time interval.)