A 6.0 * 103 kg car accelerates from rest at the top of a driveway that is sloped at an angle of 19.3 ◦ with the horizontal. An average frictional force of 4.4*103 N impedes the car's motion so that the car's speed at the bottom of the driveway is 4.3 m/s. The acceleration of gravity is 9.81 m/s 2. What is the length of the driveway? Answer in units of m.

s = 3.68 m

Explanation:

given,

mass of the car = 6 x 10³ Kg

angle of slope with horizontal = 19.3°

Average frictional force = 4.4*10³ N

Speed of the car at the bottom = 4.3 m/s

acceleration due to gravity = 9.81 m/s²

length of driveway = ?

first calculating the net force acting on the car

F = mg sin θ - f

(mg sin θ) is the weight component of the body

(f) is the frictional force which is acting opposite to the car

F = 6000 x 9.81 x sin 19.3° - 4400

F = 19454 - 4400

F = 15054 N

we know,

Force = mass x acceleration

15054 = 6000 x a

a = 2.51 m/s²

using formula

v² = u² + 2 as

4.3² = 0² + 2 x 2.51 x s

s = 3.68 m

the length of the driveway = s = 3.68 m