# Multiple step velocity/acceleration problem

• hannah2329
In summary, the train's acceleration is -.803m/s^2 and it would take 19.8 seconds for the train to come to a complete stop from its initial velocity of 26.1m/s. To find the total distance necessary, you need to add the distance traveled for the two separate accelerations, which can be calculated using average velocity and time.
hannah2329

## Homework Statement

a train is moving at 26.1m/s. 12.7 sec later its speed is 15.9m/s. find the trains acceleration- -.803m/s^2

what additional time would be necessary to bring the train to a stop if it continues to accelerate at the same rate calculated?
-.803=0-15.9/t which is 19.8 seconds

this is the part i can't figure out. i only have two tries left.

find the total distance necessary to bring the train to a complete stop from the beginning initial velocity.

## The Attempt at a Solution

i tried setting it up 26.1=d/32.5 but that wasnt right and now i don't know what else to do.

You need to add the two values of distance for the two separate accelerations.
Does the fact that distance traveled = average velocity x time help?
For both accelerations you have the initial and final velocity as well as the time.
[average velocity = 0.5 x (initial + final) ]

I understand that I'm just not sure which velocity I'm supposed to use on each step that's where I'm stuck because everytime I tried it I got the answer wrong.

a train is moving at 26.1m/s. 12.7 sec later its speed is 15.9m/s. find the trains acceleration- -.803m/s^2
1st step
velocity goes from 26.1 to 15.9m/s. What is the average?
Distance traveled = average velocity x time

what additional time would be necessary to bring the train to a stop if it continues to accelerate at the same rate calculated?
-.803=0-15.9/t which is 19.8 seconds
2nd step
Velocity goes from 15.9m/s (from part 1) to zero
What is the average velocity?
Distance is average velocity x time.

I would first clarify that the units for velocity are typically meters per second (m/s) and for acceleration are meters per second squared (m/s^2).

To solve this problem, we can first use the formula for average acceleration, which is change in velocity divided by change in time (a=Δv/Δt), to find the acceleration of the train. We are given the initial velocity (26.1 m/s) and the final velocity (15.9 m/s), as well as the time interval (12.7 seconds). Plugging these values into the formula, we get:

a = (15.9 m/s - 26.1 m/s) / (12.7 s)
a = -10.2 m/s / 12.7 s
a = -0.803 m/s^2

So, the acceleration of the train is -0.803 m/s^2.

To find the additional time needed to bring the train to a stop, we can use the formula for final velocity (v = u + at), where u is the initial velocity, a is the acceleration, and t is the time. We know that the final velocity will be 0 m/s (since the train is coming to a stop) and we can use the acceleration we just calculated (-0.803 m/s^2). Plugging in these values, we get:

0 m/s = 15.9 m/s + (-0.803 m/s^2) * t
-15.9 m/s = -0.803 m/s^2 * t
t = -15.9 m/s / (-0.803 m/s^2)
t = 19.8 seconds

So, it would take an additional 19.8 seconds for the train to come to a complete stop if it continues to accelerate at the same rate.

To find the total distance necessary to bring the train to a complete stop, we can use the formula for displacement (s = ut + 1/2at^2), where u is the initial velocity, a is the acceleration, and t is the time. Again, we know that the final velocity will be 0 m/s and we can use the acceleration we calculated earlier (-0.803 m/s^2). Plugging in these values, we get:

s = (26.1 m/s)(19.8 s) + 1

## What is a multiple step velocity/acceleration problem?

A multiple step velocity/acceleration problem involves determining the velocity and/or acceleration of an object at multiple points in time, based on given information such as initial velocity, time, and distance.

## How do I solve a multiple step velocity/acceleration problem?

To solve a multiple step velocity/acceleration problem, you need to first identify the given information and what is being asked for. Then, use the appropriate equations (such as the kinematic equations) and plug in the known values to solve for the unknown values.

## What are some common equations used to solve multiple step velocity/acceleration problems?

Some common equations used in multiple step velocity/acceleration problems include the kinematic equations (such as v = u + at and s = ut + 1/2at^2) and the formula for average velocity (v = Δs/Δt).

## What units should be used in multiple step velocity/acceleration problems?

In multiple step velocity/acceleration problems, it is important to use consistent units throughout the calculations. Common units used in these problems include meters (m) for distance, seconds (s) for time, and meters per second (m/s) for velocity.

## What are some tips for solving multiple step velocity/acceleration problems?

Some tips for solving multiple step velocity/acceleration problems include carefully reading the problem and identifying the given information and what is being asked for, drawing a diagram to visualize the problem, and using the correct equations and units. It is also important to check your answers and make sure they are reasonable based on the given information.

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