Un móvil con MRUV pasa por dospuntos con velocidades de 3 m/s y 7 m/s. Si dichos puntos están separados 50 m. ¿Qué tiempo empleó en el recorrido?

1. Break Down the Problem

To solve this problem, we will determine the time taken by an object moving with uniformly accelerated rectilinear motion (MRUV) that passes from one point to another with given velocities, covering a specific distance.

2. Relevant Concepts

For MRUV, we can use the following kinematic equation:

$d = v_i t + \frac{1}{2} a t^2$

where:

• $d$ = distance (50 m)
• $v_i$ = initial velocity (3 m/s)
• $v_f$ = final velocity (7 m/s)
• $a$ = acceleration
• $t$ = time

We can find the acceleration using the following formula which relates initial velocity, final velocity, and time:

$v_f = v_i + a t$

From this, we can express acceleration as:

$a = \frac{v_f - v_i}{t}$

3. Analysis and Detail

We're given:

• $d = 50 \, \text{m}$
• $v_i = 3 \, \text{m/s}$
• $v_f = 7 \, \text{m/s}$

Step 3.1: Find the Average Velocity

The average velocity $v_{avg}$ can be calculated as:

$v_{avg} = \frac{v_i + v_f}{2} = \frac{3 \, \text{m/s} + 7 \, \text{m/s}}{2} = \frac{10 \, \text{m/s}}{2} = 5 \, \text{m/s}$

Step 3.2: Calculate the Time

Now we can use the average velocity to find the time taken for the distance:

$t = \frac{d}{v_{avg}} = \frac{50 \, \text{m}}{5 \, \text{m/s}} = 10 \, \text{s}$

4. Verify and Summarize

We found the average velocity and used it correctly to determine the time based on the given distance. The calculations are consistent with the definitions of average velocity and time.

Final Answer

The time employed in the recorrido is $10 \, \text{s}$.