# I cant solve a simple Acceleration/Deceleration rate of time problem.

• smashbrohamme
In summary: The calculations can be simplified by converting all units to a consistent system (e.g. meters and seconds) and using the three kinematics equations mentioned. In summary, using the three kinematics equations, the minimum running time for the train to travel 7km between stations is approximately 317.2 seconds.
smashbrohamme
A train with a maximum speed of 105km/h has an acceleration rate of 0.25m/s² and a deceleration rate of 0.7 m/s². Determine the minimum running time between stations 7km apart, if it stops at all stations.

We are using the basic kinematics equations.
S= VoT + 1/2aT²
V=Vo +aT
V² = Vo² +2as

My main problem is what would acceleration be considered, I am giving two variables.
.25m/s² and -0.7 m/s².

So far I have S= 7km which I converted to 7000m
V= 105 km/h which I converted to 29.16m/s

first find the distance train travels while it accelerates to max velocity and also distance is travels while decelerating from max velocity to 0 .. rest distance left is traveled at max velocity.

Find corresponding times and add them

Ok first I took the kinematics equation V=Vo+at

29.16m/s= 0+(.25m/s²)t

T= 116.6s for the train to accelerate to a full velocity of 29.16m/s
S = 1700M for the train to travel to full acceleration.
So there is a distance of 5300M left to go.

It takes the train 607.3M to go from full velocity to 0.
T= 41.6s

4692.7M to go.

so at full velocity of 29.16m/s
I divide the 4692.7 M by 29.16m/s to get a time of 160s...

Man is there a easier way to do this, like more kinematics formulas that I might need to know?

I'm afraid No

I would suggest breaking down the problem into smaller parts to better understand and solve it. First, let's define the variables that we have been given:

- Maximum speed (Vmax) = 105 km/h = 29.16 m/s
- Acceleration rate (a) = 0.25 m/s²
- Deceleration rate (a') = 0.7 m/s²
- Distance between stations (d) = 7 km = 7000 m

Now, let's consider the train's motion between the two stations:

1. Acceleration phase: The train starts from rest (Vo = 0) and accelerates to its maximum speed (Vmax) with an acceleration rate of 0.25 m/s². Using the equation V = Vo +aT, we can find the time (T) taken for the train to reach Vmax:

Vmax = Vo + aT
29.16 = 0 + (0.25)xT
T = 116.64 seconds

2. Constant speed phase: The train travels at a constant speed of Vmax for a certain distance (d/2) between the two stations. Using the equation S = VoT + 1/2aT², we can find the distance (d/2) traveled during this phase:

d/2 = (29.16)x(116.64) + 1/2(0.25)(116.64)²
d/2 = 1698.36 + 1700.26
d/2 = 3398.62 meters

3. Deceleration phase: The train now needs to decelerate from its maximum speed (Vmax) to a complete stop at the next station, with a deceleration rate of 0.7 m/s². Using the equation V² = Vo² + 2a'S, we can find the distance (S) required for the train to come to a complete stop:

0 = (29.16)² + 2(-0.7)S
S = 120.64 meters

4. Total time taken: Now, we can find the total time taken for the train to travel between the two stations by adding the times taken for each phase:

Total time (Ttotal) = Acceleration time + Constant speed time + Deceleration time
=

## 1. What is acceleration/deceleration rate of time?

Acceleration/deceleration rate of time refers to the change in the rate at which an object's speed increases or decreases over a certain period of time. It is often measured in meters per second squared (m/s^2).

## 2. How do I calculate acceleration/deceleration rate of time?

To calculate acceleration/deceleration rate of time, you will need to know the initial and final velocity of the object, as well as the total time it takes for the object to change its speed. The formula for acceleration is: a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. What factors can affect acceleration/deceleration rate of time?

Several factors can affect acceleration/deceleration rate of time, including the mass of the object, the force acting on the object, and any external forces such as friction or air resistance.

## 4. How does acceleration/deceleration rate of time relate to an object's motion?

Acceleration/deceleration rate of time is directly related to an object's motion. If the acceleration rate is positive, the object is speeding up; if it is negative, the object is slowing down. A constant acceleration rate of time results in a linear change in an object's velocity, while a changing acceleration rate can result in curved motion.

## 5. Can acceleration/deceleration rate of time be negative?

Yes, acceleration/deceleration rate of time can be negative. This means that the object is decelerating, or slowing down, over a certain period of time. A negative acceleration rate of time is also known as deceleration or retardation.

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