A train, initially stationary, has a constant acceleration of 0.5 m/s Squared.
A) what is its speed of 15 s?
B) What would be the total time it would take to reach a speed of 25 m/s?
i want solution for this Q
To find the speed of the train at a given time, we can use the equation:
\(v = u + at\)
where:
\(v\) = final velocity (speed)
\(u\) = initial velocity (speed) = 0 m/s (since the train is initially stationary)
\(a\) = acceleration = 0.5 m/s²
\(t\) = time
A) Finding the speed at 15 s:
We substitute the given values into the equation:
\(v = 0 + (0.5 \times 15)\)
\(v = 0 + 7.5\)
\(v = 7.5\) m/s
Therefore, the speed of the train at 15 s is 7.5 m/s.
B) Finding the total time to reach a speed of 25 m/s:
In this case, we need to find the time it takes for the train to accelerate from 0 m/s to 25 m/s.
We rearrange the equation as follows:
\(t = \frac{v - u}{a}\)
where:
\(t\) = total time
\(v\) = final velocity (speed) = 25 m/s
\(u\) = initial velocity (speed) = 0 m/s
\(a\) = acceleration = 0.5 m/s²
Substituting the given values into the equation:
\(t = \frac{25 - 0}{0.5}\)
\(t = \frac{25}{0.5}\)
\(t = 50\) seconds
Therefore, the total time it would take for the train to reach a speed of 25 m/s is 50 seconds.
To solve these problems, we can use the equations of motion under constant acceleration. The equations we will use are:
1) v = u + at
2) v² = u² + 2as
3) s = ut + 0.5at²
Where:
- v represents the final velocity,
- u represents the initial velocity,
- a represents the acceleration,
- t represents the time,
- s represents the displacement.
Let's solve the problems step by step:
A) What is its speed at 15 s?
We are given:
- Initial velocity (u) = 0 m/s (as the train is initially stationary),
- Acceleration (a) = 0.5 m/s²,
- Time (t) = 15 s.
Using equation 1, we can calculate the velocity (v):
v = u + at
v = 0 + (0.5)(15)
v = 0 + 7.5
v = 7.5 m/s
Therefore, the speed of the train at 15 seconds is 7.5 m/s.
B) What would be the total time it would take to reach a speed of 25 m/s?
We are given:
- Initial velocity (u) = 0 m/s (as the train is initially stationary),
- Acceleration (a) = 0.5 m/s²,
- Final velocity (v) = 25 m/s.
Using equation 2, we can rearrange it to solve for time (t):
v² = u² + 2as
25² = 0² + 2(0.5)s
625 = s
We have found the displacement to be 625 meters. Now we can use equation 3 to find the time it takes to reach this displacement:
s = ut + 0.5at²
625 = 0t + 0.5(0.5)t²
625 = 0.25t²
t² = 2500
t ≈ 50 seconds
Therefore, the total time it would take for the train to reach a speed of 25 m/s is approximately 50 seconds.
a. Vf=a*time
b. Vf=a*time