Question

A 2.1 ✕ 103-kg car starts from rest at the top of a 5.1-m-long driveway that is inclined at 17° with the horizontal. If an average friction force of 4.0 ✕ 103 N impedes the motion, find the speed of the car at the bottom of the driveway.

Answer 1

Answer:

v = 3.135 m/s

Explanation:

given,

mass of car = 2.1 x 10³ Kg

length of driveway = 5.1 m

angle on inclination, θ = 17°

frictional force, f = 4.0 ✕ 10³ N

The force from the newton's second law

$F_{net} = m a$

$a = \dfrac{F_{net}}{m}$

$F_{net} = m g sin \theta - f_r$

$m a= m g sin \theta - f_r$

$a=\dfrac{m g sin \theta - f_r}{m}$

The speed of the car

$v = \sqrt{2as}$

$v = \sqrt{2(\dfrac{m g sin \theta - f_r}{m})s}$

$v = \sqrt{2(\dfrac{2100\times 9.81 \times sin 17^0- 4 \times 10^3}{2100})\times 5.1}$

v = 3.135 m/s

Speed of the car at the bottom of the driveway, v = 3.135 m/s