Question

periodo de 90 segundos. calcula la aceleración.

1. anthony participa en una competencia de botes. maneja a una velocidad de 58 k/h en un periodo de 10 minutos. calcula la aceleración.
2. mia es una deportista de tenis de mesa. en una competencia le pega a la y esta sale a una velocidad de 700 k/h en un periodo de 1 minuto. calcula la aceleración.
3. define aceleración.
4. ¿por qué es importante conocer sobre aceleración?
5. define velocidad.
6. escribe la fórmula para calcular aceleración.

Explanation:

Step1: Recall acceleration formula

Acceleration $a=\frac{\Delta v}{\Delta t}$, where $\Delta v$ is change in velocity and $\Delta t$ is change in time. Also need to convert units to SI - meters per second for velocity and seconds for time.

Step2: For problem 6

Initial velocity $u = 0$ (assuming starts from rest), final velocity $v = 58\ km/h$. Convert $v$ to $m/s$: $v=58\times\frac{1000}{3600}\ m/s\approx16.11\ m/s$, time $t = 10\ minutes=10\times60 = 600\ s$. Then $a=\frac{v - u}{t}=\frac{16.11-0}{600}\ m/s^{2}\approx0.027\ m/s^{2}$.

Step3: For problem 7

Initial velocity $u = 0$ (assuming starts from rest), final velocity $v = 700\ km/h$. Convert $v$ to $m/s$: $v = 700\times\frac{1000}{3600}\ m/s\approx194.44\ m/s$, time $t=1\ minute = 60\ s$. Then $a=\frac{v - u}{t}=\frac{194.44 - 0}{60}\ m/s^{2}\approx3.24\ m/s^{2}$.

Step4: Define acceleration

Acceleration is the rate of change of velocity of an object with respect to time. Mathematically, $a=\frac{\Delta v}{\Delta t}$, and it is a vector quantity, having both magnitude and direction.

Step5: Importance of knowing acceleration

Acceleration is important in understanding the motion of objects. In physics, it helps in analyzing the movement of vehicles, projectiles, and in engineering for designing machinery and transportation systems. It is also crucial in sports for athletes to optimize their performance, for example, in sprinting or in accelerating in a car - race.

Step6: Define velocity

Velocity is a vector quantity that refers to the rate at which an object changes its position. It is defined as the displacement of an object per unit time. Mathematically, $v=\frac{\Delta x}{\Delta t}$, where $\Delta x$ is the displacement and $\Delta t$ is the time interval.

Step7: Acceleration formula

The formula for calculating acceleration is $a=\frac{v - u}{t}$ or $a=\frac{\Delta v}{\Delta t}$, where $v$ is the final velocity, $u$ is the initial velocity, $\Delta v$ is the change in velocity and $t$ or $\Delta t$ is the time taken for the change in velocity.

Answer:

For problem 6: $a\approx0.027\ m/s^{2}$
For problem 7: $a\approx3.24\ m/s^{2}$
For problem 8: Acceleration is the rate of change of velocity of an object with respect to time. It is a vector quantity, $a = \frac{\Delta v}{\Delta t}$.
For problem 9: It helps in understanding motion of objects, used in physics, engineering and sports for performance - optimization.
For problem 10: Velocity is a vector quantity, the rate of change of position, $v=\frac{\Delta x}{\Delta t}$.
For problem 11: $a=\frac{v - u}{t}$ or $a=\frac{\Delta v}{\Delta t}$