Question

dos autos que están separados inicialmente (800\text{ m}) poseen rapideces constantes de (30\text{ m/s}) y (20\text{ m/s}). determine luego de qué tiempo el móvil a alcanzará al móvil b.

a) (60\text{ s})
b) (50\text{ s})
c) (80\text{ s})
d) (40\text{ s})
e) (90\text{ s})

Explanation:

🆕 New Concept Discovered: Relative Speed in Overtaking
How fast one object closes the gap on another.

Step 1: Identify the given values

We are given the following values from the problem:

• Initial separation distance between car A and car B: \( d = 800\text{ m} \)
• Constant speed of car A: \( v_A = 30\text{ m/s} \)
• Constant speed of car B: \( v_B = 20\text{ m/s} \)

Both cars are moving in the same direction.

Step 2: Calculate the relative speed

To find out how fast car A is catching up to car B, we calculate their relative speed (the rate at which the gap between them decreases):

$$ v_{\text{rel}} = v_A - v_B $$

$$ v_{\text{rel}} = 30\text{ m/s} - 20\text{ m/s} = 10\text{ m/s} $$

This means car A closes the gap by \( 10\text{ meters} \) every second.

Step 3: Calculate the time to overtake

The time (\( t \)) required for car A to cover the initial separation distance of \( 800\text{ m} \) at this relative speed is:

$$ t = \frac{d}{v_{\text{rel}}} $$

$$ t = \frac{800\text{ m}}{10\text{ m/s}} = 80\text{ s} $$

Answer:

C) 80 s