# How Far Does a Sprinter Run During Acceleration in a 100m Dash?

• nathan scott
In summary, a sprinter in a 100 m dash has an acceleration of 2.68 m/s2 to reach top speed, after which he runs with constant velocity. The total race is completed in 12.0s. The distance covered during the acceleration phase can be calculated using the equations d1=1/2*2.68 m/s2*t2 and d2=vt. By solving for d1+d2=100m, the correct value for t can be obtained.
nathan scott

## Homework Statement

In the 100 m dash a sprinter accelerates from rest to a top speed with an acceleration whose magnitude is 2.68 m/s2. After reaching top speed, he runs remainder of race with constant velocity. If total race is run in 12.0s, how far does he run during the acceleration phase?

## Homework Equations

d1= 1/2*2.68 m/s2*t2
d2= vt = 2.68 m/s2*t*12.0s - t

## The Attempt at a Solution

Not knowing if the above equations are correct I tried d1+d2=100m.
I multiplied everything, moved the 100m to the other side and tried the quadratic formula. I don't think I came out with the correct answer. I got approx. t= 3.5 or t= about 18. Any suggestions

Nevermind. I've finally figured out my errors.

?

First, it is important to note that the equations provided are not entirely correct. The first equation, d1= 1/2*2.68 m/s2*t2, is missing a term for initial velocity and should be d1= 1/2*a*t^2. The second equation, d2= vt = 2.68 m/s2*t*12.0s - t, is incorrect and should be d2= v*t, where v is the constant velocity during the second phase of the race.

To solve this problem, we can use the equation d = v0*t + 1/2*a*t^2, where d is the distance, v0 is the initial velocity, t is the time, and a is the acceleration. In this case, we know that the initial velocity is 0 m/s and the acceleration is 2.68 m/s^2. We also know that the total time is 12.0 seconds and we want to find the distance during the acceleration phase, which we can call d1.

Plugging in these values, we get d1 = 0 + 1/2*2.68 m/s^2*(12.0 s)^2 = 161.28 m. This means that the sprinter runs 161.28 meters during the acceleration phase. To find the distance during the constant velocity phase, we can simply subtract this from the total distance, which is 100 m. Therefore, the distance during the constant velocity phase is 100 m - 161.28 m = 38.72 m.

In summary, the sprinter runs 161.28 meters during the acceleration phase and 38.72 meters during the constant velocity phase, for a total distance of 200 meters. It is always important to carefully check your equations and make sure they are correct before attempting to solve a problem.

## What is the acceleration/distance problem?

The acceleration/distance problem is a physics problem that involves calculating the distance an object travels given its initial velocity, acceleration, and time. It is often used to describe the motion of objects in a straight line.

## How do you solve the acceleration/distance problem?

To solve the acceleration/distance problem, you can use the following formula: distance = initial velocity * time + (1/2) * acceleration * time^2. Simply plug in the known values for initial velocity, time, and acceleration to calculate the distance traveled.

## What is the difference between acceleration and velocity?

Acceleration is the rate at which an object's velocity changes. It is measured in meters per second squared (m/s^2). Velocity, on the other hand, is the speed and direction of an object's motion. It is measured in meters per second (m/s).

## Can you have a negative acceleration?

Yes, you can have a negative acceleration. It just means that the object is slowing down or changing direction in the opposite direction of its initial velocity. Negative acceleration is also known as deceleration.

## How does the acceleration/distance problem relate to real-life situations?

The acceleration/distance problem has many real-life applications, such as calculating the distance a car travels given its initial speed and acceleration, or determining the distance a ball will travel when thrown with a certain initial velocity. It is also used in sports, such as track and field, to analyze an athlete's performance and improve their technique.

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