Car's Total Acceleration on Curved Road: Calculate Magnitude

[jaymar023]

A car travels along a level curved road with a speed which is decreasing at a constant rate of 0.6 m/s. The speed of the car as it passes point A is 16 m/s. Calculate the magnitude of the total acceleration of the car as it passes point B which is 120 m along the road from A. The radius of curvature of the road at B is 60 m.

I am clueless about how to solve this question so if anybody can give me any hints or tips (not the answer) it would be much appreciated.

 

[tiny-tim]

A car travels along a level curved road with a speed which is decreasing at a constant rate of 0.6 m/s. The speed of the car as it passes point A is 16 m/s. Calculate the magnitude of the total acceleration of the car as it passes point B which is 120 m along the road from A. The radius of curvature of the road at B is 60 m.

Hi jaymar023!

(you mean 0.6m/s²)

Hint: call the distance along the road s.

Then you know s'' = -0.6.

And s = rθ. So θ'' = … ?

Now what are the tangential and radial accelerations in terms of r and θ?

 

[nvn]

jaymar023: The problem statement gives you a constant tangential deceleration, -0.6 m/s^2 (assuming that's what you meant to type). Do you know of a kinematics formula that relates final velocity, initial velocity, constant acceleration, and distance traveled? Also, look for a second formula that relates normal acceleration, velocity, and radius of curvature.

 

[jaymar023]

acceleration = change in velocity / time and acceleration = velocity²/ radius ?

 

[jaymar023]

actually v²= u² + 2as ?

 

[jaymar023]

So the final velocity is 10.58 m/s and the acceleration at point B = 1.87 m/s² ?

 

[nvn]

jaymar023 wrote,[/color] "v^2 = u^2 + 2*a*s, and acceleration = (velocity^2)/radius? ... So the final velocity is 10.58 m/s?"[/color]

That's correct. Normal acceleration = (velocity^2)/(radius of curvature).

jaymar023 wrote,[/color] "And the acceleration at point B = 1.87 m/s^2?"[/color]

Not quite. The question is asking for total (resultant) acceleration.

 

[jaymar023]

So the resultant acceleration is -0.6 m/s² + 1.87 m/s² = 1.27m/s²?

 

[nvn]

That's incorrect. Study "vector addition" in your textbook, and how to compute the magnitude (length) of the resulting vector when you add two vectors together. Vector addition is not the same as scalar addition.

 

[jaymar023]

Answer is 1.96m/s^2?

 

[nvn]

That's correct.