Some useful formulae: Formulae for the case of constant acceleration a 0: x(ts) = x) +va) (ts − t) + ½ a (tj − ti)² - X (ts) = x) + vu) (ts-ti) - a (ts—ti)² v (₁₁) + a(tƒ-ti) (1) t V (ts) + v(ti) (ts-ti) 2 v(ts) = X (ts) = - x(t) = x(ti) + 2a Formulae for the case of constant velocity v: x(ts) = x(t) + v(ts-ti) v(ts) = V (ti) = v Problem 2: Two cars start at the same instant from the same position, and both start from rest. Car A begins its journey at a constant acceleration and, after reaching a speed of 100 m/s in a period of 2 minutes, continues its journey at a constant speed. Car B, for its part, also begins its journey at a constant acceleration until it reaches 100 m/s; but the acceleration of B is twice that of A; as said, after reaching a speed of 100 m/s, B also continues at a constant speed. Then, a) Calculate the initial acceleration of car B. Option A: 1.67 m/s² Option B: 0 m/s² Option C: 9.8 m/s² Option D: 60 m/s² b) Calculate the distance at which car B is from car A at the moment the latter reaches its maximum speed. Option A: 6,000 m Option B: 3 km Option C: 9,000 m Option D: 2 km c) Now, suppose that a third car, let's call it C, have also started together with the other two but, unlike A and B, the car C already starts with a constant velocity ve, a velocity that will maintain throughout its entire journey. It is also known that the position of car C coincides with that of car A just at the moment when the latter reaches its maximum speed. What is the velocity v. of car C? Option A: 50 m/s Option B: 120 m/s Option C: 100 m/s Option D: 0 m/s d) The (relative) velocity that car B has with respect to the driver of car A when 300 seconds have passed since the start of the journey. Option A: 50 m/s Option B: 0 km/h Option C: 120 m/s Option D: 60 m/s e) The (relative) velocity that car B has with respect to the driver of car A when 60 seconds have passed since the start of the trip. Option A: 120 m/s Option B: 100 m/s Option C: 0 m/s Option D: 50 m/s

Some useful formulae: Formulae for the case of constant acceleration a 0: x(ts) = x) +va) (ts − t) + ½ a (tj − ti)² - X (ts) = x) + vu) (ts-ti) - a (ts—ti)² v (₁₁) + a(tƒ-ti) (1) t V (ts) + v(ti) (ts-ti) 2 v(ts) = X (ts) = - x(t) = x(ti) + 2a Formulae for the case of constant velocity v: x(ts) = x(t) + v(ts-ti) v(ts) = V (ti) = v Problem 2: Two cars start at the same instant from the same position, and both start from rest. Car A begins its journey at a constant acceleration and, after reaching a speed of 100 m/s in a period of 2 minutes, continues its journey at a constant speed. Car B, for its part, also begins its journey at a constant acceleration until it reaches 100 m/s; but the acceleration of B is twice that of A; as said, after reaching a speed of 100 m/s, B also continues at a constant speed. Then, a) Calculate the initial acceleration of car B. Option A: 1.67 m/s² Option B: 0 m/s² Option C: 9.8 m/s² Option D: 60 m/s² b) Calculate the distance at which car B is from car A at the moment the latter reaches its maximum speed. Option A: 6,000 m Option B: 3 km Option C: 9,000 m Option D: 2 km c) Now, suppose that a third car, let's call it C, have also started together with the other two but, unlike A and B, the car C already starts with a constant velocity ve, a velocity that will maintain throughout its entire journey. It is also known that the position of car C coincides with that of car A just at the moment when the latter reaches its maximum speed. What is the velocity v. of car C? Option A: 50 m/s Option B: 120 m/s Option C: 100 m/s Option D: 0 m/s d) The (relative) velocity that car B has with respect to the driver of car A when 300 seconds have passed since the start of the journey. Option A: 50 m/s Option B: 0 km/h Option C: 120 m/s Option D: 60 m/s e) The (relative) velocity that car B has with respect to the driver of car A when 60 seconds have passed since the start of the trip. Option A: 120 m/s Option B: 100 m/s Option C: 0 m/s Option D: 50 m/s

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section: Chapter Questions

Problem 23P: The driver of a car slams on the brakes when he sees a tree blocking the road. The car slows...

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