1.A train passes an electric post in 8sec and a bridge of length 1km in 108sec .Find the speed of the engine .
2.A runner travels at the rate o f25km/hr for 4min ;then at 50km/hr for 8minn and finally at 20km/hr for 2min .Find a) the total distance covered in km and b)average speed in m/sec
1. L is the length of the train.
The speed of the train is v = L/8,
The time of passing the bridge begins when head end of the train enters the bridge and ends when the rear end leaves the bridge, therefore, the speed of the train is
(s+L)/108.
L/8 = (s+L)/108
L/8 – L/108 = s/108.
s =1000 m
L = 69 m.
v = 69/8 = 8.6 m/s.
2. v1 = 25 km/hr = 25000/3600 =6.94 m/s.
s1 =v1•t1 = 6.94•4•60 =1666 m.
v2 = 50 km/hr = 50000/3600 = 13.9 m/s. (actually, it’s impossible since the world record of Usain Bolt is 9.58 s for 100 m. that gives speed 100/9.58 =10.44 m/s !!!!!)
s2 = v2•t2 = 13.9•8•60 =6667 m.
v3 = 20 km/hr =20000/3600 =5.56 m/s.
s3 = v3•t3 = 25.56•2•60 =667 m
Total distance is
s =s1+s2+s3 = 1666 + 6667 +667 =9000 m.
Total time is
t =t1+t2+t3 = 14•60 =840 sec.
v = s/t =9000/840 = 10.7 m/s.
(actually, all this is impossible since the world record of Usain Bolt is 9.58 s for 100 m. That gives the speed 100/9.58 =10.44 m/s !!!!!)
To find the speed of the engine in question 1, we can use the formula:
Speed = Distance / Time
First, let's find the distance covered when the train passes the electric post. Since we are only interested in the speed of the engine, we don't need to know the length of the train. Let's assume the distance covered when the train passes the electric post is 'x'.
The time it takes for the train to pass the electric post is given as 8 seconds. So we can write the equation:
x = Speed * 8 --- (1)
Next, let's find the distance covered when the train passes the bridge. The length of the bridge is given as 1km. So the distance covered when passing the bridge is 1km. The time it takes to pass the bridge is given as 108 seconds. We can write another equation:
1 = Speed * 108 --- (2)
Now we have two equations with two unknowns (x and Speed). We can solve these equations to find the speed of the engine.
From equation (1), we have:
x = 8 * Speed
Substituting this into equation (2):
8 * Speed = 1
Divide both sides by 8:
Speed = 1/8
Therefore, the speed of the engine is 1/8 km/second or 0.125 km/second.
For question 2, we are given different speeds and durations of time. To find the total distance covered, we can calculate the distance covered in each segment of time and add them together.
First, let's calculate the distance covered in the first segment:
Speed = 25 km/hr
Time = 4 minutes = 4/60 hours (converted to hours)
Distance1 = Speed * Time = 25 * (4/60) = 25/15 = 5/3 km
Next, let's calculate the distance covered in the second segment:
Speed = 50 km/hr
Time = 8 minutes = 8/60 hours (converted to hours)
Distance2 = Speed * Time = 50 * (8/60) = 400/60 = 20/3 km
Finally, let's calculate the distance covered in the third segment:
Speed = 20 km/hr
Time = 2 minutes = 2/60 hours (converted to hours)
Distance3 = Speed * Time = 20 * (2/60) = 40/60 = 2/3 km
To find the total distance covered, we add the distances from each segment:
Total Distance = Distance1 + Distance2 + Distance3 = (5/3) + (20/3) + (2/3) = 27/3 = 9 km
To find the average speed, we can use the formula:
Average Speed = Total Distance / Total Time
First, let's calculate the total time covered:
Total Time = 4 + 8 + 2 = 14 minutes = 14/60 hours (converted to hours)
Average Speed = 9 / (14/60) = 540/14 = 270/7 m/sec
Therefore, the average speed is 270/7 m/sec.