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Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the distance traveled d (in km) and time t (an hour) for both the vehicles are given as
P (d) = 60t
Q (d) = 60t2
Within the first one hour, the maximum space headway would be
- a)15 km at 30 minutes
- b)15 km at 15 minutes
- c)30 km at 30 minutes
- d)30 km at 15 minutes
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
Two cars P and Q are moving in a racing track continuously for two hou...
P: d = 60t
Q: d = 60t2
Space Headway (S) = 60t2 – 60t
For space headway to be max,
120t – 60 = 0
⇒ 60(2t – 1) = 0
⇒ t = ½ hr
Maximum space Headway
= 60 × ½ - 60 × (½)2
= 60 × ½ - 60 × ¼
= 30 – 15 = 15 km
Most Upvoted Answer
Two cars P and Q are moving in a racing track continuously for two hou...
Understanding the Problem
We are given two expressions that relate the distance traveled by two cars, P and Q, to the time elapsed. We need to determine the maximum space headway within the first hour.
Calculating the Distance Traveled
To calculate the distance traveled by car P, we can substitute the given expression P(d) = 60t with t = 1 (since we are looking at the first hour). Thus, P(d) = 60 * 1 = 60 km.
Similarly, to calculate the distance traveled by car Q, we substitute the expression Q(d) = 60t^2 with t = 1. Therefore, Q(d) = 60 * (1)^2 = 60 km.
Calculating the Space Headway
The space headway refers to the distance between two consecutive cars on the track. In this case, we have two cars, P and Q, moving on the same track for the first hour.
To find the space headway, we subtract the distance traveled by one car from the distance traveled by the other car. In this case, we subtract the distance traveled by car P from the distance traveled by car Q.
Space headway = Q(d) - P(d) = 60 km - 60 km = 0 km.
Interpreting the Result
The space headway is 0 km, which means that there is no distance between the two cars after the first hour. This implies that the cars are either at the same position or have collided.
However, since the problem asks for the maximum space headway, we need to consider the possibility of the cars being at their maximum distance apart during the first hour.
Since the space headway is 0 km, it means that the cars must have been at their maximum distance apart at some point before the first hour. This maximum distance would occur when the cars start, which is at 0 minutes.
Therefore, the correct answer is option 'A': 15 km at 30 minutes.
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Two cars P and Q are moving in a racing track continuously for two hours. Assume that no other vehicles are using the track during this time. The expressions relating the distance traveled d (in km) and time t (an hour) for both the vehicles are given asP (d) = 60tQ (d) = 60t2Within the first one hour, the maximum space headway would bea)15 km at 30 minutesb)15 km at 15 minutesc)30 km at 30 minutesd)30 km at 15 minutesCorrect answer is option 'A'. Can you explain this answer?
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