Find the least acceleration and least retardation?

[Douna2nd]

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?

 

[tiny-tim]

Hi Douna2nd!

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

(use the standard https://www.physicsforums.com/newreply.php?do=newreply&p=4423610 equations)

 

[Douna2nd]

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

 

[tiny-tim]

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?

… 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

you knew u v and s, and you wanted a, so the correct formula would be … ?

 

[Douna2nd]

V^2 =Vo^2 +2 a S
I solved the problem in a wrong way in the exaaaaam! :O

 

[tiny-tim]

'fraid so!

but hopefully you've done well in the rest of the exam ​

 

[Douna2nd]

Why is the velocity zero in the second case? The car will be moving but moving slowly

 

[tiny-tim]

Why is the velocity zero in the second case? The car will be moving but moving slowly

no …

… 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

 

[Douna2nd]

Aahh! Thank you ! :D