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 train travelling at a speed of 72 km/hr crosses a post in 20 seconds. If it crosses another train travelling at a speed of 54 km/hr in the same direction in 1 minute 45 seconds, then the difference in length between the two trains is
Rajiv's boat can travel along the current at the 8 km/hour and against the current at the rate 6 km/hour. Find the time taken by the boat to sail 28 km in still water.
Rohit and Dinesh are 64 km apart. Rohit can walk at a speed of 15 km/hr and Dinesh at the speed of 17 km/hr. In how many hours will they meet if they are travelling towards each other?
Two trains running in opposite directions cross a man standing on the platform in 25 seconds and 32 seconds respectively and they cross each other in 30 seconds. The ratio of their speed is:
A worker covers a distance of 81 km in 11 hours. He travels partly on foot at 4.5 km/h and partly on bicycle at 15 km/h. What is the distance covered on the cycle?
