# Acceleration, distance, time. help.

• Eagleized
In summary, the first car will travel a distance of 558.46 ft before catching up to the second car which is traveling at a speed of 132 f/s.
Eagleized

## Homework Statement

vehicle 1 is traveling at a constant speed of 90mph (132 f/s) 5 seconds before vehicle 2 begins to accelerate from 0-90 mph taking 17.09 seconds to do so. how far a distance will vehicle 2 travel while accelerating to 90mph. and how long will it take for vehicle 2 to catch up to vehicle 1 while accelerating at approximately 5.2 m/s/s or 15.6 f/s

## Homework Equations

The relationship between the 2 vehicles is dependant.

what is the total distance traveled by vehicle 2 before it catches up to vehicle 1?

## The Attempt at a Solution

ok, it's too hard to explain and argue at the same time, so i'll leave it at this:
find a function of position for car #1 and car #2, call them c_1(t) and c_2(t), set them equal and solve for t. what does this mean exactly?
This should help you a bit, at constant acceleration, call it a, the position of car 2 at time t is at^2/2
the first car, meanwhile is moving at a constant velocity v, so its position at time t is vt
does car 2 start from rest?
so solve vt=at^2/2 -> at^2-vt=0 -> use quadratic formula
this will give you the time t, when car 2 catches up to car 1, ?? to answer part 2 of the Q

For your first question you could use the equation Vf^2 = Vi^2 + 2(a)(d) where Vf is the final velocity, Vi is the initial velocity, a is the acceleration, and d is the displacement.

For number 2, since the first car is traveling at constant speed we can label the distance it travels as d = V(t + 5) while we may use the equation df = (a)(t^2)/2 + (Vi)t + di. Equate the two and solve for the time.

did you get a distance of 4044.8 ft for the first part of the question?

or 558.46 ft?

Last edited:
anyone get an answer for this?

## 1. What is acceleration and how is it calculated?

Acceleration is the rate of change of velocity over time. It is calculated by dividing the change in velocity by the change in time. 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.

## 2. How does distance affect acceleration?

The distance an object travels does not directly affect its acceleration. However, if the object travels a longer distance in the same amount of time, its average velocity will be higher, resulting in a higher acceleration.

## 3. Is acceleration always constant?

No, acceleration is not always constant. It can be either constant or changing. An object with a constant acceleration will have a steady change in velocity, while an object with a changing acceleration will have a varying change in velocity over time.

## 4. How is acceleration related to force?

Acceleration is directly proportional to force. This means that the greater the force applied to an object, the greater its acceleration will be. This relationship is described by Newton's second law of motion, which states that F = ma, where F is force, m is mass, and a is acceleration.

## 5. What is the relationship between acceleration, distance, and time?

The relationship between acceleration, distance, and time can be described by the formula d = vit + 1/2at^2, where d is distance, vi is initial velocity, t is time, and a is acceleration. This equation shows that the distance an object travels is dependent on its initial velocity, the time it takes to travel, and its acceleration.

Replies
8
Views
712
Replies
24
Views
7K
Replies
5
Views
2K
Replies
2
Views
2K
Replies
6
Views
358
Replies
6
Views
1K
Replies
6
Views
1K
Replies
9
Views
2K
Replies
5
Views
908
Replies
1
Views
1K