How Long Does It Take for a Car to Catch Up to a Truck?

[muktl]

a car is going at 90 km/h

a truck is 50 km/h

the car is 100m behind the truck

so how long does the car need to reach to the truck?

 

[maverick_starstrider]

This should be in the homework help section. but first try writing an equation for the position of the car as a function of time and then write an equation for the position of the truck as a function of time plus 100m (this way the position of the truck is relative to the initial position of the car). Now, when they meet they meet at the same time and the same position so then simply equate the two equations to find the time.

 

[nlightner]

In order to solve this problem, we need to first convert the speeds of the car and truck from kilometers per hour (km/h) to meters per second (m/s). This will make it easier to calculate the time needed for the car to reach the truck.

To convert km/h to m/s, we can use the formula: m/s = (km/h) x (1000 m/1 km) x (1 hour/3600 seconds). This gives us a conversion factor of 0.2778.

So, the car's speed in m/s is 90 km/h x 0.2778 = 25 m/s.

Similarly, the truck's speed in m/s is 50 km/h x 0.2778 = 13.89 m/s.

Now, we can use the formula for velocity (v = d/t) to find the time needed for the car to reach the truck. We know that the car is 100m behind the truck, so the distance (d) between them is 100m. We also know the velocity (v) of the car (25 m/s) and truck (13.89 m/s). Plugging these values into the formula, we get:

25 m/s = 100m/t (since the car is catching up to the truck, we can assume they have the same time t)

Solving for t, we get t = 4 seconds.

Therefore, it will take the car 4 seconds to reach the truck. It is important to note that this calculation assumes that the car and truck are traveling at constant speeds and in a straight line. Any changes in speed or direction can affect the time needed for the car to reach the truck.