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
- Daksh travels 200 km at 50 km/hr, the next 252 km at 42 km/hr and the next 204 km at 51 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
- A bus travelling at 66 km/hr completes a journey in 15 hours. What should be its speed to cover the same distance in 5 hours?
- Train A leaves station M at 8:00 a.m. and reaches station N at 3:00 p.m. on the same day. Train B leaves station N at 10:00 a.m. and reaches station M at 3:00 p.m. on the same day. Find the time when Trains A and B meet.
- A bus travelling at 95 km/hr completes a journey in 10 hours. What should be in its speed to cover the same distance in 5 hours?
Rishi travels 198 km at 66 km/hr, the next 584 km at 73 km/hr and the next 656 km at 82 km/hr. What is his average speed (in km/hr) for the whole journey? (Round off your answer to two decimal places)
