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Two cars are moving towards each other on a straight road with velocity 10 m/s and
12m/s respectively. When they are 160m apart, then each car decelerates at
2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest.
Verified Answer
Two cars are moving towards each other on a straight road with velocit...
Let first car be c1 and second be c2.
C1:
u = 10
v= 0
a= - 2
Since v^2 = u^2 + 2as
=) 0^2 = 10^2 + 2*-2*s
=) 0 = 100 - 4s
=) 4s = 100
=) s = 100/4 = 25m.
Hence distance covered by car 1 will be 25m.
C2:
u = - 12(because of opposite motion of direction by C1)
v = 0
a = - 2
Since v^2 = u^2 + 2as
=) 0^2 = 12^2 + 2*-2*s
=) 0 = 144 - 4s
=) 4s = 144
=) s = 144/4 = 36m.
Hence distance covered by C2 will be 36m.
Hence total distance travel by them = 25+36 = 61m.
=) Distance between them when they come to rest = 160m - 61m
= 99m.
This question is part of UPSC exam. View all NEET courses
Most Upvoted Answer
Two cars are moving towards each other on a straight road with velocit...
Initial Conditions
- Car A is moving towards Car B with a velocity of 10 m/s.
- Car B is moving towards Car A with a velocity of 12 m/s.
- The initial distance between the two cars is 160 meters.
Deceleration Phase
- Both cars begin to decelerate at a rate of 2 m/s² until they come to a complete stop.
Time to Stop
- For Car A:
- Initial velocity (u) = 10 m/s
- Final velocity (v) = 0 m/s
- Deceleration (a) = 2 m/s²
- Time (t) = (v - u) / a = (0 - 10) / -2 = 5 seconds
- For Car B:
- Initial velocity (u) = 12 m/s
- Final velocity (v) = 0 m/s
- Deceleration (a) = 2 m/s²
- Time (t) = (v - u) / a = (0 - 12) / -2 = 6 seconds
Distance Covered During Deceleration
- For Car A:
- Distance (s) = ut + (1/2)at² = 10(5) + 0.5(-2)(5²) = 50 - 25 = 25 meters
- For Car B:
- Distance (s) = ut + (1/2)at² = 12(6) + 0.5(-2)(6²) = 72 - 36 = 36 meters
Total Distance Covered
- Total distance covered by both cars = 25 meters (Car A) + 36 meters (Car B) = 61 meters
Final Distance Between Cars
- Remaining distance between the cars when they come to rest = Initial distance - Total distance covered
- Remaining distance = 160 meters - 61 meters = 99 meters
Conclusion
- The distance between the two cars when they come to rest is 99 meters.
- Car A is moving towards Car B with a velocity of 10 m/s.
- Car B is moving towards Car A with a velocity of 12 m/s.
- The initial distance between the two cars is 160 meters.
Deceleration Phase
- Both cars begin to decelerate at a rate of 2 m/s² until they come to a complete stop.
Time to Stop
- For Car A:
- Initial velocity (u) = 10 m/s
- Final velocity (v) = 0 m/s
- Deceleration (a) = 2 m/s²
- Time (t) = (v - u) / a = (0 - 10) / -2 = 5 seconds
- For Car B:
- Initial velocity (u) = 12 m/s
- Final velocity (v) = 0 m/s
- Deceleration (a) = 2 m/s²
- Time (t) = (v - u) / a = (0 - 12) / -2 = 6 seconds
Distance Covered During Deceleration
- For Car A:
- Distance (s) = ut + (1/2)at² = 10(5) + 0.5(-2)(5²) = 50 - 25 = 25 meters
- For Car B:
- Distance (s) = ut + (1/2)at² = 12(6) + 0.5(-2)(6²) = 72 - 36 = 36 meters
Total Distance Covered
- Total distance covered by both cars = 25 meters (Car A) + 36 meters (Car B) = 61 meters
Final Distance Between Cars
- Remaining distance between the cars when they come to rest = Initial distance - Total distance covered
- Remaining distance = 160 meters - 61 meters = 99 meters
Conclusion
- The distance between the two cars when they come to rest is 99 meters.
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Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest.
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Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest..
Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest. for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest. covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars are moving towards each other on a straight road with velocity 10 m/s and12m/s respectively. When they are 160m apart, then each car decelerates at2m/s.s until they stop in order to avoid collision. Calculate the distance between them when they come to rest..
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