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Two cars A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,, op.1.d<2.5m op.2.d="">125cm,, op.3. d>25cm,, op.4.d<125m.?>
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Two cars A and B are moving in same direction with velocities 30m/s an...
Problem: Two cars A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,
Solution:
Step 1: Find the time taken by car A to come to rest
Initial velocity of car A, u = 30m/s
Retardation of car A, a = 2m/s^2
Using the formula v^2 = u^2 + 2as, where v = 0 (final velocity) and s is the distance travelled by car A before coming to rest, we get:
0 = 30^2 - 2 x 2 x s
s = 450m
Using the formula v = u + at, where v = 0 (final velocity) and u = 30m/s, we get:
t = u/a
t = 15 seconds
Step 2: Find the distance travelled by car B during the time taken by car A to come to rest
Distance travelled by car B, d = u x t
d = 20 x 15
d = 300m
Step 3: Determine the minimum distance required between car A and car B to avoid collision
Let the minimum distance between car A and car B be x
During the time taken by car A to come to rest, car B will cover a distance of 300m. Therefore, the total distance covered by car B before coming to rest will be:
300 + x
Using the formula v^2 = u^2 + 2as, where u = 20m/s, a = -2m/s^2 (negative because car B is also decelerating due to friction) and v = 0, we get:
0 = 20^2 - 2 x (-2) x (300 + x)
0 = 400 + 1200 + 4x
x = 125m
Therefore, the minimum distance required between car A and car B to avoid collision is 125m or 12500cm.
Step 4: Check the given options
- Option 1: d < 125cm
- Option 2: d = 125cm
- Option 3: d > 25cm
- Option 4: d = 25cm
Solution:
Step 1: Find the time taken by car A to come to rest
Initial velocity of car A, u = 30m/s
Retardation of car A, a = 2m/s^2
Using the formula v^2 = u^2 + 2as, where v = 0 (final velocity) and s is the distance travelled by car A before coming to rest, we get:
0 = 30^2 - 2 x 2 x s
s = 450m
Using the formula v = u + at, where v = 0 (final velocity) and u = 30m/s, we get:
t = u/a
t = 15 seconds
Step 2: Find the distance travelled by car B during the time taken by car A to come to rest
Distance travelled by car B, d = u x t
d = 20 x 15
d = 300m
Step 3: Determine the minimum distance required between car A and car B to avoid collision
Let the minimum distance between car A and car B be x
During the time taken by car A to come to rest, car B will cover a distance of 300m. Therefore, the total distance covered by car B before coming to rest will be:
300 + x
Using the formula v^2 = u^2 + 2as, where u = 20m/s, a = -2m/s^2 (negative because car B is also decelerating due to friction) and v = 0, we get:
0 = 20^2 - 2 x (-2) x (300 + x)
0 = 400 + 1200 + 4x
x = 125m
Therefore, the minimum distance required between car A and car B to avoid collision is 125m or 12500cm.
Step 4: Check the given options
- Option 1: d < 125cm - This option is not possible as the minimum distance required is 12500cm.
- Option 2: d = 125cm - This option is correct as it satisfies the minimum distance requirement.
- Option 3: d > 25cm - This option is correct as it satisfies the minimum distance requirement.
- Option 4: d = 25cm -
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Two cars A and B are moving in same direction with velocities 30m/s an...
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Two cars A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,, op.1.d125cm,, op.3. d>25cm,, op.4.d
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Two cars A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,, op.1.d125cm,, op.3. d>25cm,, op.4.d 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 A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,, op.1.d125cm,, op.3. d>25cm,, op.4.d covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two cars A and B are moving in same direction with velocities 30m/s and 20m/s. When car A is at a distance d behind the car B, the driver of the car A applies brakes producing uniform retardation of 2m/s^2. There will be no collision when,, op.1.d125cm,, op.3. d>25cm,, op.4.d.
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