What is the car's acceleration just before emerging from the turn?

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In summary, the problem involves a car entering a curve at 27 m/s with a radius of 126 m. The driver applies the brakes, causing a constant tangential deceleration of 1.2 m/s^2. The question asks for the magnitude of the car's acceleration just before emerging from the turn. The solution involves using the formula v^2 = u^2 + 2as to find the final velocity, taking into account the distance traveled and initial velocity. The tangential acceleration is not zero, while the radial acceleration can be calculated using centripetal acceleration.
  • #1
mujadeo
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Homework Statement



A car moving at a speed of 27 m/s enters a curve that describes a quarter turn of radius 126 m. The driver gently applies the brakes, giving a constant tangential deceleration of magnitude 1.2 m/s2.


Homework Equations



a) Just before emerging from the turn, what is the magnitude of the car's acceleration?

The Attempt at a Solution



heres what i know, but can't seem to put it all together for this problem.
v-initial = 27m/s
v-final (as it emerges from the turn) = ?
a = 1.2 (the radial acceleration component has to be zero because it is going round an arc right? (pie/2 .. also s = 197.9m )
(the tangetial acceleration is the one that changes, correct?)

I need to find v-final but how can i do that without the time?

Please help!
 
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  • #2
You can re-arange s = u t + 0.5 a t^2 to give
v^2 = u^2 + 2 a S (Sorry for not putting it into latex)

Good start is to write down all the numbers you know, or can easily work out.
 
  • #3
mujadeo said:
(the radial acceleration component has to be zero because it is going round an arc right? (pie/2 .. also s = 197.9m )
(the tangetial acceleration is the one that changes, correct?)
Not correct--just the opposite! The tangential acceleration is given as constant--the tangential speed changes, of course. The radial acceleration is not zero! Hint: How do you calculate centripetal acceleration?

I need to find v-final but how can i do that without the time?
Use the distance.
 
  • #4
Isn't the corner a red herring?

Distance = 0.2 * 2pi*126 m
U = 27
a = 1.2 m/s^2

v =
 
Last edited:
  • #5
mgb_phys said:
Isn't the corner a red herring?
Not at all. Note that they take care to specify "Just before emerging from the turn..."

(And the OP had already calculated the distance.)
 

1. How does a car go around a corner?

When a car approaches a corner, it must slow down in order to maintain control and avoid skidding. The driver turns the steering wheel in the direction they want to go, causing the front wheels to turn. This changes the direction of the car and allows it to navigate the corner.

2. What factors affect a car's ability to go around a corner?

There are several factors that can affect a car's ability to go around a corner, including the speed of the car, the condition of the road, the weight distribution of the car, the type of tires, and the angle of the corner. These factors can impact the car's stability and traction, making it easier or more difficult to navigate the turn.

3. Why do some cars take corners better than others?

The design and engineering of a car can greatly impact its ability to take corners. Factors such as weight distribution, suspension system, and tire grip can all contribute to a car's handling and cornering abilities. Cars that are specifically designed for performance and racing often have features that allow them to take corners at higher speeds and with more precision.

4. How does a car's speed affect its ability to go around a corner?

The speed of a car is a crucial factor when it comes to going around a corner. If a car is traveling too fast, it may lose traction and slide or skid. This is because the centrifugal force created by the car's speed can overcome the friction between the tires and the road. Slowing down before a corner allows the car to maintain control and navigate the turn safely.

5. What should I do if my car starts to skid while going around a corner?

If your car starts to skid while going around a corner, the most important thing to do is to remain calm and avoid overreacting. Do not brake or accelerate, as this can make the skid worse. Instead, gently steer in the direction of the skid and gradually slow down until you regain control of the car. It is also important to make sure your tires are properly inflated and in good condition to prevent skidding in the first place.

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