# Suvat - Two cars approach each other on a straight road

Suvat -- Two cars approach each other on a straight road

## Homework Statement

Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at 4m/s^2. Where and when do the cars collide?

## Homework Equations

I'm assuming that this would result in a simultaneous equation given that there are two unknowns; distance (s) and time (t) (where and when).

## The Attempt at a Solution

CAR A
s = s
u = 16m/s
v = x
a = -2m/s^2
t = t

s = ut + 1/2 at^2
s = 16t - t^2
Equation 1

CAR B
s = s
u = 8m/s
v = x
a = -4m/s^2
t = t

s = ut + 1/2 at^2
s = 8t - 2t^2
Equation 2

Equation 1: s = 16t - t^2
Equation 2: 2s = 16t - 4t^2

It is at this point I fall as I still land up with two unknown variables: -s = 5t^2

Where am I going wrong?

## The Attempt at a Solution

Let the distance traveled by car A before collision be sA and that by car B be sB. The total distance sA + sB should be 45 (why?).

Now write sA and sB in terms of t and simplify.

gneill
Mentor

Be sure to check the velocities of each car at the calculated time of collision. Why? Because you need to make sure that the result you obtain is physically meaningful in the context of the problem.

Your equations imply that both cars moving in same direction and start to slow down at same location where t=0, s=0 for both.
At t=0 they are 45m apart and opposite direction.

One of the equations is correct, say car A.
The other ,car B, should have value at t=0, s=45m.
As they approach each other, car A should have increasing distance from origin(until it starts to reverse) and car B decreasing value until it starts reversing too.

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I think I get it now. Are the answers;
t = 3s and s = 39m

gneill
Mentor

I think I get it now. Are the answers;
t = 3s and s = 39m
Did you check the velocities of the two cars at this time of impact?

should they be the same?

gneill
Mentor

should they be the same?
What do you think? Hint: Are you sure that BOTH cars will still be moving at the time of collision? Is it possible for one car to come to a halt (from braking) before the other?

I think I get it now. Are the answers;
t = 3s and s = 39m
http://img684.imageshack.us/img684/6497/collidingcars2.jpg [Broken]
http://img36.imageshack.us/img36/5285/collidingcars.jpg [Broken]

It is a piecewise function not purely parabolic function.
Both have maximum distance travelled. No reversing.
Thanks gneill, it's really tricky question.

Last edited by a moderator:
pbuk
Gold Member
What is car B's velocity after 2s?

PeterO
Homework Helper

## Homework Statement

Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at 4m/s^2. Where and when do the cars collide?
Did you check to see if the cars actually collide at all.

How far will Car A have travelled by the time it stops, if Car B didn't exist.
How far will Car B travel before it stops, if Car A didn't exist.

If those two distances total less than 45m, the cars simply stop.

Which car would have stopped first?

Would that car have stopped before the other collided with it? (if there was a collision)

Amoghha
Suvat -- Two cars approach each other on a straight road

## Homework Statement

Two cars approach each other on a straight road. Car A is moving at 16m/s and car B at 8m/s. When they are 45m apart both drivers apply their brakes. Car A slows down at a rate of 2m/s^2 while car B slows down at 4m/s^2. Where and when do the cars collide?

## Homework Equations

I'm assuming that this would result in a simultaneous equation given that there are two unknowns; distance (s) and time (t) (where and when).

## The Attempt at a Solution

CAR A
s = s
u = 16m/s
v = x
a = -2m/s^2
t = t

s = ut + 1/2 at^2
s = 16t - t^2
Equation 1

CAR B
s = s
u = 8m/s
v = x
a = -4m/s^2
t = t

s = ut + 1/2 at^2
s = 8t - 2t^2
Equation 2

Equation 1: s = 16t - t^2
Equation 2: 2s = 16t - 4t^2

It is at this point I fall as I still land up with two unknown variables: -s = 5t^2

Where am I going wrong?

## Homework Equations

3. The
See take the motion of car A first and denote distance travelled by it as sA

For Car A
u = 16
v= o
a= -2
use v=u+at and solve for t
t = 8 sec ( time taken by car A to stop)

now calculate distance travelled by car A during this time (sA)

S = ut + 1/2at^2
solve it for s
you get sA = 44

Do the same thing for car B and now sum up sA and sB you get where they will meet and sum up their times you get when they meet.

attempt at a solution