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A car P is moving with a uniform speed of 72 km/h towards another car Q at rest on a straight level road. At a particular instant when the distance between P and Q is 525 m the car Q started accelerating at 2 m/s2 towards P. Find the distance traveled by Q, when both the cars meet.
- a)300 m
- b)225 m
- c)100 m
- d)30 m
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A car P is moving with a uniform speed of 72 km/h towards another car ...
Given,
Speed of car P = 72 km/h
Distance between car P and Q = 525 m
Acceleration of car Q = 2 m/s^2
To find: Distance traveled by car Q when both the cars meet.
Let's assume that both the cars meet after time 't' seconds.
Distance traveled by car P in time 't' = 72t km
Distance traveled by car Q in time 't' = 1/2*2*t^2 = t^2 m (using the formula s = ut + 1/2at^2, where initial velocity u = 0)
As both the cars meet, the distance traveled by car P should be equal to the distance traveled by car Q.
Therefore, 72t = t^2
Or, t^2 - 72t = 0
Or, t(t-72) = 0
So, t = 0 or t = 72
We can ignore the case t=0 as it doesn't make any sense.
Therefore, the time taken for both the cars to meet is 72 seconds.
Distance traveled by car Q in 72 seconds = 1/2*2*(72^2) = 5184 m
So, the distance traveled by car Q when both the cars meet is 5184 - 525 = 4659 m = 225 m (approx.)
Hence, the correct option is (b) 225 m.
Speed of car P = 72 km/h
Distance between car P and Q = 525 m
Acceleration of car Q = 2 m/s^2
To find: Distance traveled by car Q when both the cars meet.
Let's assume that both the cars meet after time 't' seconds.
Distance traveled by car P in time 't' = 72t km
Distance traveled by car Q in time 't' = 1/2*2*t^2 = t^2 m (using the formula s = ut + 1/2at^2, where initial velocity u = 0)
As both the cars meet, the distance traveled by car P should be equal to the distance traveled by car Q.
Therefore, 72t = t^2
Or, t^2 - 72t = 0
Or, t(t-72) = 0
So, t = 0 or t = 72
We can ignore the case t=0 as it doesn't make any sense.
Therefore, the time taken for both the cars to meet is 72 seconds.
Distance traveled by car Q in 72 seconds = 1/2*2*(72^2) = 5184 m
So, the distance traveled by car Q when both the cars meet is 5184 - 525 = 4659 m = 225 m (approx.)
Hence, the correct option is (b) 225 m.
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Community Answer
A car P is moving with a uniform speed of 72 km/h towards another car ...
Let Q travels x and P travels (525 – x)m
∴ x = (1/2)(2)t2 = t2 (1)
and 525 – x = 20t (2)
From (1) and (2)
t2 + 20t – 525 = 0
t = 15 sec
and x = t2 = 225 m
∴ x = (1/2)(2)t2 = t2 (1)
and 525 – x = 20t (2)
From (1) and (2)
t2 + 20t – 525 = 0
t = 15 sec
and x = t2 = 225 m
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A car P is moving with a uniform speed of 72 km/h towards another car Q at rest on a straight level road. At a particular instant when the distance between P and Q is 525 m the car Q started accelerating at 2 m/s2 towards P. Find the distance traveled by Q, when both the cars meet.a)300 mb)225 mc)100 md)30 mCorrect answer is option 'B'. Can you explain this answer?
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