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(10 pts.) A car of mass m is on an icy driveway inclined at an angle .
(A)Find the acceleration of the car, assuming the driveway is frictionless.
(B) Suppose the car is released from rest at the top of the incline and the distance from the car’s front
bumper to the bottom of the incline is d. How long does it take the front bumper to reach the
bottom of the hill, and what is the car’s speed as it arrives there?

Respuesta :

okpalawalter8

The acceleration and time is mathematically given as

a=gsinθ

[tex]t=\frac{2d}{gsinθ}[/tex]

What is the acceleration of the car, assuming the driveway is frictionless, and how long does it take the front bumper to reach the bottom of the hill, and what is the car’s speed as it arrives there?

Generally, the equation for the Force of the car is mathematically given as

[tex]N = mg cos\theta[/tex]

Therefore

[tex]ma=mgsin\theta[/tex]

a=gsinθ

The acceleration of the car is mathematically given as

a=gsinθ

Generally, the equation for the final velocity of the car is mathematically given as

[tex]v^2−u^2=2as[/tex]

Therefore

[tex]v 2 −(0) 2 =2(gsin\theta)d[/tex]

[tex]v= \sqrt {2gsin\theta.d}[/tex]

​

Generally, the equation for the motion of the car is mathematically given as

v−u=at

[tex]2gsin\thetad =(gsin\theta)t[/tex]

[tex]t=\frac{2d}{gsinθ}[/tex]

In conclusion, the time it takes the front bumper to reach the bottom of the hill is

[tex]t=\frac{2d}{gsinθ}[/tex]

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