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Name: Two sports cars (A and B) are racing on a straight track of length 5 k
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Description: Two sports cars (A and B) are racing on a straight track of length 5 km. Initially, two cars were at rest. Once the race starts, both cars are accelerating uniformly before they gain their maximum velocities. After each car reaches its maximum veloci

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Two sports cars (A and B) are racing on a straight track of length 5 km. Initially, two cars were at rest. Once the race starts, both cars are accelerating uniformly before they gain their maximum velocities. After each car reaches its maximum velocity, it moves with the same speed during the rest of the race. Given that car A accelerates for 1min with 0.2 m/s²acceleration and car B has an acceleration of 0.15 m/s²for a period of 100 s.

(A) Which car wins the race? What is the time difference between the events as the two cars pass the finish line?

(B) If exists, at what time the velocities of the two cars become equal to each other?

(D) If both cars need to finish the race at the same time, what would be the new acceleration of the previously lost car while accelerating the same time duration. (Consider that the car who one the previous race doesn't change its parameters)

Expert Solution

Step 1 Finding the Maximum Velocities of two cars

For Car A, it is given that

Acceleration, $a_{A} = 0.2 m / s^{2}$

Acceleration time, ${}^{t}A = 1 m i n = 60 s$

By using the relation, $v = u + a t$ , we have

$v_{A} = u_{A} + a_{A} t_{A}$ where $v_{A}$ and $u_{A}$ are the final and initial velocity. Since the car was at rest initially, $u_{A} = 0$

$v_{A} = a_{A} t_{A} = 0.2 m / s^{2} \times 60 s = 12 m / s$

For Car B, it is given that

Acceleration, $a_{B} = 0.15 m / s^{2}$

Acceleration time, ${}^{t}B = 100 s$

By using the relation, $v = u + a t$ , we have

$v_{B} = u_{B} + a_{B} t_{B}$ where $v_{B}$ and $u_{B}$ are the final and initial velocity. Since the car was at rest initially, $u_{B} = 0$

$v_{B} = a_{B} t_{B} = 0.15 m / s^{2} \times 100 s = 15 m / s$

Therefore, the maximum velocities attained by car A and car B are

$v_{A} = 12 m / s v_{B} = 15 m / s$

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