Solving a Car's Acceleration in a Quarter Turn

In summary, The problem involves a car moving at a speed of 35 m/s entering a curve with a radius of 130 m. The driver applies the brakes with a constant tangential deceleration of 1.2 m/s^2. The question is asking for the magnitude of the car's acceleration just before exiting the turn. To find this, we need to calculate the vector sum of the centripetal acceleration and the tangential acceleration.
  • #1
Northstar
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Hi all, I can't figure out what the next step is on a problem. The problem is:
A car moving at a speed of 35 m/s enters a curve that describes a quarter turn of radius 130 m. The driver gently applies the brakes, giving a constant tangential deceleration of magnitude 1.2 m/s^2. Just before emerging from the turn, what is the magnitude of the car's acceleration?

I found that Vf = 27.1 and that the centripetal acceleration was 5.65 m/s^2 (I am not positive these are correct, however). I am stuck on what I do next in the question. Any help would be greatly appreciated.
 
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  • #2
The total acceleration will be the vector sum of the centripital acceleration (which acts in which direction?), and the tangential acceleration (which acts in the direction of the tangent to the circle). To calculate the "magnitude" of the car's acceleration, do the vector addition of the two components, and then take the magnitude of that resultant vector.
 
  • #3
Awesome, thanks!
 

FAQ: Solving a Car's Acceleration in a Quarter Turn

How do you calculate a car's acceleration in a quarter turn?

The acceleration of a car in a quarter turn can be calculated by dividing the change in velocity by the time it takes to complete the turn. This can be represented by the formula: a = Δv/t, where a is the acceleration, Δv is the change in velocity, and t is the time.

What factors affect a car's acceleration in a quarter turn?

The acceleration of a car in a quarter turn can be affected by several factors such as the car's mass, the friction between the tires and the road, and the direction and magnitude of the centripetal force acting on the car.

Can a car accelerate in a quarter turn without any external forces?

No, a car cannot accelerate in a quarter turn without any external forces. In order for a car to change its direction and accelerate, there must be a net external force acting on it, such as the centripetal force provided by the friction between the tires and the road.

How does the radius of the turn affect a car's acceleration?

The radius of the turn has a direct impact on a car's acceleration. A smaller radius means a sharper turn, which requires a higher centripetal force and therefore a higher acceleration. On the other hand, a larger radius allows for a more gradual turn and a lower acceleration.

What is the difference between tangential acceleration and centripetal acceleration?

Tangential acceleration is the component of acceleration that is parallel to the direction of motion, while centripetal acceleration is the component of acceleration that is perpendicular to the direction of motion and towards the center of the turn. In the case of a car's acceleration in a quarter turn, the tangential acceleration is typically constant, while the centripetal acceleration varies based on the radius of the turn.

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