Find the least acceleration and least retardation?

In summary, the driver of a car traveling at 10 m/sec with 3 seconds left before a red light has two choices: to accelerate and reach the crossing before the light changes, or to stop at the light. The least acceleration needed in the first case can be found using the equation S=Vot + 1/2 a t^2, while the least deceleration needed in the second case can be found using the equation V^2 =Vo^2 +2 a S. The correct formula for finding deceleration in the second case is the latter one, as the car will need to come to a complete stop by the time it reaches the light.
  • #1
Douna2nd
20
0
A car is traveling at 10 m/sec. When it is 40 meters from a crosswalk, there is still 3 seconds before the light changes to red. The driver has two choices: the first is to accelerate to reach the crossing before the light changes to red and the second is to try to stop at the light. What is the least acceleration which would be necessary in the first case? And what is the least retardation which would be necessary in the second case?
 
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  • #2
Hi Douna2nd! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

(use the standard https://www.physicsforums.com/newreply.php?do=newreply&p=4423610 equations)
 
  • #3
It was in my final exam today actually and I did in the first case S=Vot + 1/2 a t^2 and I have the distance, the intial velocity and time and I got the a then in the second case I didn't actually know what to do but I assumed that S =0 and used the same rule used above and got the acceleration but I wanted to know what is the correct answer for this problem
 
  • #4
Douna2nd said:
A car is traveling at 10 m/sec. When it is 40 meters from a crosswalk, there is still 3 seconds before the light changes to red.
… the second is to try to stop at the light. … what is the least retardation which would be necessary in the second case?
Douna2nd said:
… in the second case I didn't actually know what to do but I assumed that S =0 and used the same rule used above and got the acceleration but I wanted to know what is the correct answer for this problem

nooo, s is still 40, v is 0 :redface:

you knew u v and s, and you wanted a, so the correct formula would be … ? :smile:
 
  • #5
V^2 =Vo^2 +2 a S
I solved the problem in a wrong way in the exaaaaam! :O
 
  • #6
'fraid so!

but hopefully you've done well in the rest of the exam :smile:​
 
  • #7
Why is the velocity zero in the second case? The car will be moving but moving slowly
 
  • #8
Douna2nd said:
Why is the velocity zero in the second case? The car will be moving but moving slowly

no …
Douna2nd said:
… the second is to try to stop at the light.

… if she stops at (or before) the light, her speed is 0 at (or before) the light

the least deceleration will be the one that makes her speed 0 at the light :wink:
 
  • #9
Aahh! Thank you ! :D
 

Related to Find the least acceleration and least retardation?

1. What is acceleration and retardation?

Acceleration is the rate of change of velocity over time, while retardation (or deceleration) is the rate of decrease in velocity over time.

2. How do you find the least acceleration and least retardation?

To find the least acceleration and least retardation, you would need to measure the initial and final velocities of an object, as well as the time it takes to change from the initial to the final velocity. Then, you can use the formula a = (vf - vi)/t to calculate the acceleration, and r = (vi - vf)/t to calculate the retardation.

3. What are some real-life examples of acceleration and retardation?

Acceleration and retardation are present in many everyday activities, such as driving a car (acceleration when pressing the gas pedal, retardation when applying the brakes), throwing a ball (acceleration when releasing the ball, retardation when it hits a surface), and riding a roller coaster (acceleration when going up a hill, retardation when going down a hill).

4. What factors can affect the least acceleration and least retardation?

The least acceleration and least retardation can be affected by various factors such as the mass of the object, the force applied, and the surface on which the object is moving. In general, a greater force or a smaller mass will result in a higher acceleration, while a smaller force or a greater mass will result in a lower acceleration.

5. Why is it important to find the least acceleration and least retardation?

Knowing the least acceleration and least retardation can help us understand and predict the motion of objects, and can also be used in engineering and design to ensure the safety and efficiency of machines and structures. It is also important in fields such as physics and mechanics, where the study of motion is a fundamental aspect.

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