Question

in forecast of a long slope of 7 degrees a bus driver accelerates to a constant ratio of 0.92m / s2 when it is still in a flat section of the road. If you know that the speed of the bus is 26.82 m / s when you start to climb the slope and the driver does not change the position of your acceleration or change speed. Determine:

a) The distance traveled by the bus on the slope when its speed has decreased to 22.35 m / s

b) The total distance traveled by the bus on the slope

c) The friction force between the bus and the slope

d) The time when the bus stops on the slope

Answer 1

Using newton's law

ma - mg*sin7 = ma'

a' = a - gsin 7

a = 0.92 - 9.8*sin 7

a = -0.2743 m/s²

using kinematics

v² - u² = 2ad

22.35² - 26.82² = 2(-0.2743)*d

d = 400.63 m

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Total distance travelled means distance travelled till the final velocity is zero

0² - 26.82² = 2(-0.2743)*d

d = 1311.2 m

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Force of friction,

equating all horizontal forces

F_friction + mgsin7 = ma

mass of bus is not given in the question

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time when the bus stops means when the final velocity is zero.

v = u + at

t = u / a

t = 98 sec