IIT JEE , AIEEE Forum - Physics , Mechanics

vikhi72

Two cars are travelling

towards

each other on a straight line

at

velocities 10m/s &12m/s.

when

they are 150m apart , both

drivers apply their brakes

and

each car decelerates at

2m/s^2

until it stops.how far apart

will

they be when they have

both

come to rest??

vikhi72

pls help me??expertz

vikhi72

pls help

dhwanitmunshi

89 m apart
rate me plss

bhuvana89

intial distance bet the two = 150 m

when brakes are applied ,

for car 1:

v^2 = u^2 + 2 (-a) s

since v=0

s= u^2/2a

so stopping distance =( 10 * 10)/ 2 * 2

= 25 m

similarly for car 2:

stopping distance = (12*12)/2*2

= 36 m

so separation between cars when they've stopped = 150 - (36 + 25 )m

= 89 m

elessar_iitkgp

The correct solution is posted below.

bhuvana89

yes......

ellessar_iitkgp is right.......!!!!

good answer sir .....!!!!

snandkeolyar

ellessar_iitkgp is completely wrong.The cars were at a distance of 150 m initially and they are travelling towards each other.so the distance between them must reduce(it should be less than 150m).So how come it is 210.5 m
the cars were at a distance 150m
for car1,
u=10m/s
v=0
a=-2m/s^2
therefore s1=-100/-4=25m
for car2,
u=12m/s
v=0
a=-2m/s^2
therefore s2=-144/-4=36m
hence final distance between them=150-(25+36)=89m

elessar_iitkgp

Time for the stopping of first car
T₁ = 10/2 = 5s
And that for the second car,
T₂ = 12/2 = 6s

Now position of first particle at this time
x₁ = (10)(5) - (1/2)2(25) = 25 m
Position of the second particle,
x₂ =150 -(12)(6) + (1/2)2(36) = 114 m

Distance between them,
d = |x₁ - x₂| = 89 m.

I forgot that they were cars and not particles moving with given accelerations. The difference with cars is that the decceleration can be assumed to be zero at the moment it stops. For particle we can assume that they start moving backwards once they stop. The relative velocity approach would be incorrect here as the relative velocity is zero at t=5.5 s. At that time first car has actually stopped. So relative velocity isn't zero at that point. So the error.

Thanx for pointing out the mistake.

gomurali

relative initial velocity is 10+12 = 22
relative acceleration is = 4
distance traveled by both before stopping is 0 - 22^2 = 2*4*s
s = 484/8 = 60.5. Therefore final separation between them = 150 - 60.5 = 89.5m

gomurali

relative initial velocity is 10+12 = 22
relative acceleration is = 4
distance travelled by both before stopping is 0 - 22^2 = 2*4*s
s = 484/8 = 60.5. Therefore final separation between them = 150 - 60.5 = 89.5m

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