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A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds?
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A bus begin to move with an acceleration of 1m/s^2 a man who is 48m be...
Problem:
A bus begins to move with an acceleration of 1m/s^2. A man who is 48m behind the bus is running at 10 m/s to catch the bus. The man will be able to catch the bus after how many seconds?
Solution:
Step 1: Determine the distance traveled by the bus before the man catches it
As the man runs towards the bus, the bus is also moving away from the man. Hence, the distance the man needs to cover to catch the bus is equal to the distance traveled by the bus plus the initial distance between the man and the bus.
Let's assume that the man is able to catch the bus after t seconds. Hence, the distance traveled by the bus in t seconds can be calculated using the following formula:
d = ut + (1/2)at^2
Where,
- d = distance traveled by the bus in t seconds
- u = initial velocity of the bus (0 m/s)
- a = acceleration of the bus (1 m/s^2)
- t = time taken by the bus to cover the distance
Substituting the values in the formula, we get:
d = 0t + (1/2)(1)t^2
d = (1/2)t^2
Step 2: Determine the distance traveled by the man before he catches the bus
As the man is running towards the bus, the distance traveled by the man can be calculated using the following formula:
d = ut
Where,
- d = distance traveled by the man in t seconds
- u = initial velocity of the man (10 m/s)
- t = time taken by the man to cover the distance
Substituting the values in the formula, we get:
d = 10t
Step 3: Equate the distance traveled by the man and the bus
As the man catches the bus, the distance traveled by the man is equal to the distance traveled by the bus. Hence, equating the two distances, we get:
(1/2)t^2 = 10t + 48
Simplifying the equation, we get:
t^2 - 20t - 96 = 0
On solving the quadratic equation, we get two values of t, i.e.,
- t = 24 seconds
- t = -4 seconds (rejected as time cannot be negative)
Step 4: Conclusion
Hence, the man will be able to catch the bus after 24 seconds.
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A bus begin to move with an acceleration of 1m/s^2 a man who is 48m be...
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A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds?.
A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds? for Class 9 2025 is part of Class 9 preparation. The Question and answers have been prepared according to the Class 9 exam syllabus. Information about A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds? covers all topics & solutions for Class 9 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bus begin to move with an acceleration of 1m/s^2 a man who is 48m behind the bus running at 10 m/s to catch the bus the man will be able to catch the bus after how many seconds?.
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