To find out how long it will take for the car to overtake the truck, we need to determine the distance it needs to cover first.
Let's denote:
- Car length = Lc = 3m
- Truck length = Lt = 10m
- Car velocity = Vc = 100km/h
- Truck velocity = Vt = 50km/h
- Initial distance between the car and the truck = d = 10m
The car needs to cover a distance of (d + Lt) to overtake the truck completely. Therefore, the distance to be covered is (10m + 10m) = 20m.
Now, let's calculate the time it takes for the car to overtake the truck.
Speed is measured in kilometers per hour (km/h), but we need to convert it to meters per second (m/s) for consistency.
Speed in m/s = (Speed in km/h) * (1,000 m / 1 km) * (1 h / 3,600 s)
Therefore,
Vc = 100 km/h * (1,000 m / 1 km) * (1 h / 3,600 s) = 27.8 m/s
Vt = 50 km/h * (1,000 m / 1 km) * (1 h / 3,600 s) = 13.9 m/s
Since both the car and the truck are moving in the same direction, the relative velocity of the car with respect to the truck is:
Relative velocity = Vc - Vt = 27.8 m/s - 13.9 m/s = 13.9 m/s
To calculate the time needed, we use the equation:
Time = Distance / Relative velocity
Therefore,
Time = 20m / 13.9 m/s ≈ 1.44 seconds
So, it will take approximately 1.44 seconds for the car to overtake the truck.