Question

As a train accelerates away from a station, it reaches a speed of 4.9 m/s in 5.1 s. If the train's acceleration remains constant, what is its speed after an additional 7.0s has elapsed?

Answer 1

The speed of the rain after accelerating for addition $7\text{ s}$ will be $\boxed{11.62\text{ m/s}}$.

Explanation:

Given:

The speed of the train after $5.1\text{ s}$ is $4.9\text{ m/s}$.

The initial speed of the train is $0\text{ m/s}$.

Concept:

The acceleration of a body is defined as the rate at which the velocity of the body in motion changes every second. If the acceleration of the body is in the direction of motion of the body, the body will be accelerated.

As the train stars from rest and accelerates away from the station, the speed of the train will increase according to the first equation of motion.

The expression for the first equation of motion for the motion of the train is:

$\boxed{v_f=v_i+at}$

Here, $v_f$ is the final speed of the train, $v_i$ is the initial speed of the train, $a$ is the acceleration of the train and $t$ is the time taken by the train.

Substitute the values of velocity for first $5.1\text{ s}$ of motion of the train.

$\begin{aligned}4.9&=0+a.(5.1)\\a&=\dfrac{4.9}{5.1}\text{ m/s}^2\\&=0.96\text{ m/s}^2\end{aligned}$

Now, the for the speed of the train after it travels for addition $7.0\text{ s}$ or a total of $12.1\text{ s}$.

$\begin{aligned}v_f&=0+(0.96)(12.1)\text{ m/s}\\v_f&=11.62\text{ m/s}\end{aligned}$

Thus, The speed of the rain after accelerating for addition $7\text{ s}$ will be $\boxed{11.62\text{ m/s}}$.

Learn More:

1. The change in motion that produces positive acceleration brainly.com/question/4508162

2. The acceleration of the box under friction brainly.com/question/7031524

3. The stone is thrown vertically upwards brainly.com/question/343100

Answer Details:

Grade: Senior School

Subject: Physics

Chapter: Laws of motion

Keywords:

train, accelerates, constant, rest, equation of motion, initial, final, velocity, time taken, addition 7 seconds, acceleration.

Answer 2

Acceleration is the rate of change of the velocity of a moving object. To determine the speed the object has at a certain time, we need to determine the acceleration first by dividing the speed with the time given. We do as follows:

acceleration = 4.9 m/s / 5.1 s = 0.96 m/s^2

To determine the velocity after 7.1 s, we multiply 7.1 s to the acceleration. 

speed or velocity = 0.96 x 7.1 = 6.52 m/s