What is the acceleration of the car?

[tica86]

A car is slides down an icy driveway that slopes at an angle of 10 degrees. What is the acceleration of the car?


Is the correct answer a=1.70m/s^2?
If it is can someone explain how they figure it out, thanks!

 

[Ambidext]

Forces acting on the car:

Weight = mg
Normal = mg cos 10 (deg)
Horizontal = mg sin 10

ma_car = mg sin 10

cancel out m,

a_car = g sin 10 = 1.7 m s^-2

So yes, 1.7.

 

[tica86]

Forces acting on the car:

Weight = mg
Normal = mg cos 10 (deg)
Horizontal = mg sin 10

ma_car = mg sin 10

cancel out m,

a_car = g sin 10 = 1.7 m s^-2

So yes, 1.7.

Ok, thanks. I have another question:

Find the net force (in Newtons) required to accelerate a 110 kg bike and rider from rest to a final velocity of 22.7 m/s in 10 seconds?

since f=ma 110(22.7)=2497 do I divide that by 10 seconds??

 

[The legend]

not exactly...

first solve for average acceleration using equations of motion...
then use the F=m*a and get your answer!

 

[rwisz]

The correct answer for the acceleration of the car is 1.70 m/s^2. To calculate this, we can use the formula for acceleration, which is a = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time taken for the change in velocity.

In this scenario, we can assume that the car starts from rest (vi = 0) and reaches a final velocity as it slides down the icy driveway. The final velocity can be calculated using the equation vf = vicosθ, where vi is the initial velocity and θ is the angle of the slope (10 degrees in this case).

Thus, vf = (0)m/s x cos10 = 0 m/s. This means that the car's velocity remains constant throughout its motion down the slope.

Next, we need to calculate the time taken for the car to reach the bottom of the slope. This can be done using the equation t = d/vf, where d is the distance traveled by the car and vf is the final velocity.

As we do not have the distance traveled, we can use the trigonometric relationship tanθ = opposite/adjacent to calculate the distance. In this case, the opposite side is the height of the driveway and the adjacent side is the length of the driveway. So, tan10 = h/L, where h is the height of the driveway and L is the length.

Rearranging this equation, we get h = Ltan10. We can assume that the driveway is 10 meters long and the height is 1.7 meters (as tan10 = 0.176 and 0.176 x 10 = 1.76). So, the distance traveled by the car is 1.7 meters.

Now, we can plug in the values in the equation t = d/vf. So, t = 1.7m/0m/s = undefined. This means that the time taken for the car to reach the bottom of the slope is 0 seconds.

Finally, we can use the formula for acceleration a = (vf - vi)/t to calculate the acceleration. As we have already calculated that vf = 0 m/s and vi = 0 m/s, the equation becomes a = (0 - 0)/0, which is undefined.

However, in physics, we can use the concept of limits to calculate the acceleration in this scenario.