# A basic velocity/distance traveled problem (need work checked)

• Whitishcube
In summary, the car in this scenario starts from rest and accelerates uniformly for 10 seconds, reaching a velocity of 100 km/hr. Using the equations of motion, the distance traveled is 138.89 meters and the average velocity is 13.89 m/sec. Alternatively, using calculus, the distance is calculated to be 1250/9 meters and the average velocity is also 13.89 m/sec. Both methods yield the same results.
Whitishcube

## Homework Statement

A car starts from rest and reaches a velocity of 100 km/hr after accelerating uniformly for 10 seconds. how far has the car gone? what is its average velocity?

## The Attempt at a Solution

so since this car accelerates uniformly, i assume that it means it has a constant acceleration, meaning the velocity is a linear equation. converting the final velocity to m/sec, i got 250/9 m/sec.

the slope of this line is then 25/9 (using equation for slope, (y_2-y_1)/(x_2-x_1), plugging in values of 250/9 for final velocity and 0 for initial, 10 for final time and 0 for initial).

then the equation for velocity is then (25/9)t.
so,
distance=integral of (25/9)t from t=0 to t=10, yielding an answer of 1250/9 meters, or about 138.89 meters.

for the second part, i just divide this integral by the difference of the two endpoints of the interval; namely 10 and 0.

avg value = integral of (25/9)t from 0 to 10, divided by 10.
this gives me the average velocity, 13.89 m/sec.

am I on the right track here?

Last edited:
Looks good to me.

EDIT: already checked, never mind. I personally find the equations of motion simpler for a situation such as this, but if that's how feel more comfortable go for it.

My answers agree with yours and so I'd say it looks good.

this is true, jarednjames, but i find it a lot simpler to use calculus... just my mindset at least. :P

thanks for the responses!

Your approach is correct, but there are a few minor errors in your calculations.

First, the conversion from 100 km/hr to m/sec should be 100,000/3600 = 250/9 m/sec, not 250/9 m/sec.

Second, the equation for velocity should be v = (25/9)t + v0, where v0 is the initial velocity (in this case, 0). So the distance traveled would be the integral of (25/9)t from t=0 to t=10, which gives an answer of 1250/9 meters, or about 138.89 meters, as you correctly calculated.

For the average velocity, you should divide the total distance traveled (1250/9 m) by the total time elapsed (10 seconds), giving an average velocity of 125/9 m/sec, or about 13.89 m/sec.

Overall, you are on the right track and have a good understanding of the concepts involved in solving this problem. Just be sure to double check your calculations and units to avoid any minor errors.

## What is a basic velocity/distance traveled problem?

A basic velocity/distance traveled problem is a mathematical problem that involves calculating the velocity or speed at which an object is moving, as well as the distance it has traveled in a given amount of time. It is commonly used in physics and other scientific fields to understand the motion of objects.

## How do you solve a basic velocity/distance traveled problem?

To solve a basic velocity/distance traveled problem, you will need to know the initial velocity (often denoted as v0), final velocity (v), time taken (t), and distance traveled (d). Use the formula d = v0t + 1/2at2 to solve for any missing variable, where a is the acceleration of the object.

## What units are used in a basic velocity/distance traveled problem?

The units used in a basic velocity/distance traveled problem will depend on the specific problem and the units given for each variable. However, some common units used in these types of problems include meters (m) for distance, meters per second (m/s) for velocity, and seconds (s) for time.

## What are some real-life applications of basic velocity/distance traveled problems?

Basic velocity/distance traveled problems have many real-life applications. For example, they can be used to analyze the motion of objects in sports, such as calculating the speed of a baseball pitch or the distance a basketball travels when thrown. They are also used in everyday situations, such as calculating the time it takes to travel to a destination based on a given speed and distance.

## Can a basic velocity/distance traveled problem be solved using different formulas?

Yes, there are multiple formulas that can be used to solve a basic velocity/distance traveled problem, depending on the given variables and what is being solved for. Some other commonly used formulas include v = d/t and vf = v0 + at, among others.

Replies
2
Views
535
Replies
3
Views
1K
Replies
15
Views
1K
Replies
4
Views
959
Replies
4
Views
2K
Replies
13
Views
2K
Replies
4
Views
796
Replies
9
Views
1K
Replies
6
Views
1K
Replies
14
Views
1K