A 3 m long car goes past a 4 m long truck at rest on the road. The speed of the car is 7 m/s. The time taken to go past is
1 s
This problem involves calculating the time it takes for one object (a car) of a certain length to completely pass another object (a truck) of a certain length that is stationary.
Understanding Passing Time
When a car passes a truck, the total distance the car needs to cover relative to the truck is the sum of their lengths. Imagine the moment the front of the car reaches the back of the truck. For the car to completely pass the truck, the back of the car must reach the front of the truck.
The total distance the car travels relative to the stationary truck to achieve this passing is the length of the car plus the length of the truck.
Car and Truck Dimensions and Speed
- Length of the car \(L_{car} = 3\) m
- Length of the truck \(L_{truck} = 4\) m
- Speed of the car \(v_{car} = 7\) m/s
- Speed of the truck \(v_{truck} = 0\) m/s (since it is at rest)
Calculating Total Distance and Relative Speed
The total distance that needs to be covered for the car to completely pass the truck is the sum of their lengths:
\[ \text{Total Distance} = L_{car} + L_{truck} \]
\[ \text{Total Distance} = 3 \text{ m} + 4 \text{ m} = 7 \text{ m} \]
Since the truck is at rest, the relative speed of the car with respect to the truck is simply the speed of the car.
\[ \text{Relative Speed} = v_{car} - v_{truck} = 7 \text{ m/s} - 0 \text{ m/s} = 7 \text{ m/s} \]
Calculating Time Taken to Pass
The time taken for the car to pass the truck is calculated using the formula:
\[ \text{Time} = \frac{\text{Total Distance}}{\text{Relative Speed}} \]
Plugging in the values we found:
\[ \text{Time} = \frac{7 \text{ m}}{7 \text{ m/s}} \]
\[ \text{Time} = 1 \text{ s} \]
Therefore, the time taken for the car to go past the truck is 1 second.
| Parameter | Value |
|---|---|
| Car Length | 3 m |
| Truck Length | 4 m |
| Car Speed | 7 m/s |
| Truck Speed | 0 m/s |
| Total Distance to Pass | \(3 \text{ m} + 4 \text{ m} = 7 \text{ m}\) |
| Relative Speed | \(7 \text{ m/s} - 0 \text{ m/s} = 7 \text{ m/s}\) |
| Time Taken | \(7 \text{ m} / 7 \text{ m/s} = 1 \text{ s}\) |
The calculated time taken matches one of the given options.
Important Questions from Speed Time and Distance
A journey of 900 km is completed in 11 h. If two-fifth of the journey is completed at the speed of 60 km/h, at what speed (in km/h) is the remaining journey completed?
A car starts from point A towards point B, travelling at the speed of 20 km/h. 1 \(\frac{1}{2}\) hours later, another car starts from point A and travelling at the speed of 30 km/h and reaches 2 \(\frac{1}{2}\) hours before the first car. Find the distance between A and B.
A bus covered a distance of 162 km. If speed of this bus is 15 m/s, then what will be the time taken ?
An athlete runs an 800 m race in 96 seconds. His speed (in km / h) is:
A person has to cover a distance of 150 km in 15 hours. If he traveled with the speed of 11.8 km/hr for 10 hours. At what speed he has to travel to cover the remaining distance in the remaining time?
