Physics Fundamentals
Physics Fundamentals
2nd Edition
ISBN: 9780971313453
Author: Vincent P. Coletta
Publisher: PHYSICS CURRICULUM+INSTRUCT.INC.
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Chapter 2, Problem 38P

(a)

To determine

The time taken by the first car to move after the second car begin to pass the first car.

(a)

Expert Solution
Check Mark

Answer to Problem 38P

The time taken by the first car to move after the second car passes through it is 1.21s .

Explanation of Solution

Given:

The time difference between the two cars is 0.500s .

Formula Used:

The time taken by the first car is 0.500s more than the second car, thus the distance travelled by the first car is given by,

  s1=v1x0(t+0.65s)+12a(t+0.5s)2

The expression for the distance travelled by the second car is given by,

  s2=v2x0t+12(2a)t2

The expression for the relation between the distance travelled by both the cars is calculated as,

  s1=s2

Calculation:

The first car starts from the rest, thus the initial velocity of the first car is v1x0=0m/s .

The distance travelled by the first car is calculated as,

  s1=v1x0(t+0.65s)+12a(t+0.5s)2=(0)(t+0.65s)+12a(t+0.5s)2=12a(t+0.5s)2

The second car starts from the rest, thus the initial velocity of the second car is v2x0=0m/s .

The distance travelled by the second car is calculated as,

  s2=v2x0t+12(2a)t2=(0)t+12(2a)t2=at2

The time after which the first car begins to move after the second car passes is given by,

  s1=s212a(t+0.5s)2=at2t+0.5=2tt=1.21s

Conclusion:

Therefore, the time taken by the first car to move after the second car passes through it is 1.21s .

(b)

To determine

The ratio for the speed of both the car at the time t=1.21s .

(b)

Expert Solution
Check Mark

Answer to Problem 38P

The ratio of the final speed of both the car is 1.41 .

Explanation of Solution

Formula Used:

The expression for the final velocity of the first car is given by,

  v1x=v1x0+2at

The expression for the final velocity of the second car is given by,

  v2=v2x0+a(t+0.5)

Calculation:

The final velocity of the first car is calculated as,

  v1x=v1x0+2at=(0m/s)+2at=2at

The final velocity of the second car is calculated as,

  v2=v2x0+a(t+0.5)=0+a(t+0.5)=a(t+0.5)

The ratio of the velocity is calculated as,

  v 1xv 2x=2ata( t+0.5)=2a( 1.21s)a( ( 1.21s )+0.5)=1.41

Conclusion:

Therefore, the ratio of the final speed of both the car is 1.41 .

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