Can Braking Distance and Reaction Time Prevent a Car Accident?

[nasadall]

A car is driven along a straight and level road at a steady speed of 25ms^-1 when the driver suddenly notices thet there is a fallen tree blocking the road 65 meters ahead. The driver immediately applies the brakes giving the car a constant retardation of 5ms^-2.

a) How far in front of the tree does the car comes to a halt?

b) If the driver had not reacted immediately and the brakes were applied one second later, with what speed would the car have hit the tree?


For a) i used equation v²=u²+2as
To find the distance traveled until the car was stoped, subtracting that distance with the 65 meters.

I don't know how to fit that into the equation or if i have to do it seperatly.

As for b) i think i have to use the same equation, but to find final velocity, somehow i don't get a good answer.


a)
0² = 25²+2(-5)s
0 = 625+(-10)s
10s = 0-625
s = -625/-10
s = 62.5 meters

65-62.5 = 2.5 meters that the car came to a halt from the tree.

b) this is what i tried, don't think its right

v² = 25²+2(-5)40
v² = 625+(-10)40
v² = 625+(-400)
v² = 225
v = sqare root of 225 = 15

i think i got it.

i take it that the distance from when the driver spoted the tree (65 meters) minus the one second which equals to 25ms is 40 meters.

Please help me

Thank You

This is for a school assignment.

 

[p21bass]

Part a looks correct. For part b - how far is the car away from the tree, if the driver waits one second (at 25m/s) before braking? Then, how fast is he/she driving at that distance?

 

[nasadall]

Thank you, part a i think is the correct answer, it makes sense for me, but i don't know if i have to subtract after or within the equation.

e don't study for about 15 years, then decite to go back to school, it's even harder then i thought.

thank you for your help

 

[zgozvrm]

First of all, determine how far the car would travel in the 1 second that the driver waits to start braking. Then how far is the tree from the car?

 

[zgozvrm]

Note that in part (a) (which you solved correctly, by the way), if you had set s to 65m and tried to solve for v, you would find that the right side of the equation would be negative, and therefore unsolvable (with real numbers). This indicates that the car would have stopped before hitting the tree.

In part (b) try setting s to the distance the tree is from the car when the driver starts braking. You should find that the right side of the equation is positive, indicating that the driver will hit the tree. So, solve for v.

(If the right side of the equation calculates to zero, that would indicate that the car would come to a stop exactly when it hits the tree).