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

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
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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
Transcribed Image Text: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
Transcribed Image Text: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
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