How Long Until the Second Car Overtakes the First?

  • Thread starter Thread starter skoomafiend
  • Start date Start date
  • Tags Tags
    Formula Kinematic
Click For Summary

Homework Help Overview

The problem involves two cars accelerating from rest, with the first car starting earlier than the second. The first car accelerates at 3 m/s², while the second car accelerates at 5 m/s² after a 6-second delay. The objective is to determine how long it takes for the second car to overtake the first car.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using kinematic equations to find the positions of both cars and equate them to determine the time of overtaking. There are attempts to express the time variables in relation to each other, particularly noting the 6-second delay of the second car.

Discussion Status

Some participants have provided equations to set up the problem, while others express confusion regarding the interpretation of the distance and time variables. There is an ongoing exploration of the mathematical relationships without a clear consensus on the solution or the correctness of the approaches taken.

Contextual Notes

Participants are working under the constraints of the problem as stated, with some questioning the accuracy of their calculations compared to a provided answer in a textbook. There is a noted uncertainty regarding the application of the kinematic equations and the setup of the problem.

skoomafiend
Messages
33
Reaction score
0

Homework Statement



A car starts from rest and accelerates uniformly at 3 m/s2. A second car starts from rest 6 s later at the same point and accelerates uniformly at 5 m/s2. How long does it take the second car to overtake the first car?
How would I solve this? If someone can break it down step by step, it would be great.

Homework Equations


x=x0 + v0t + 1/2at2

The Attempt at a Solution



I tried solving it by using the above formula and solving for t. Didnt quite work out.

car 1's time = car two's time +6 and then solving for t.
 
Physics news on Phys.org
Find the position of the first car. Then, use that distance and set it equal to the position equation of the second car to find the time.
 
I don't understand what you are saying, can you clarify please? How would I find the distance with the information given?
 
Find the velocity of the first
 
find the position of the first car in relation to what? the initial 6 second lead?
 
Correct, the position with the 6 second lead
 
(3/2)t2= (5/2)(t- 6)2

I've tried solving for this, doesn't seem to match that answer given at the back of the book.
Am I doing something wrong?
 
What's the answer? Where are you getting those numbers?
 
a1=3m/s2
a2=5m/s2

t2=(t1- 6) ...t1 is the time for the first car, then t2 left 6 seconds after the car, so it had ( t1- 6 ) seconds to get to the same position (at which point it would overtake car1)

x = x0 + v0t + 1/2at12
x = 0 + 0 + 1/2(3)t12
x = (3/2)t12

and for car two it is..

x = 0 + 0 + 1/2(5)( t1 - 6 )2
x = (5/2)( t1 - 6 )2

so that means that x would be the same distance, given these times

(3/2)t12 = (5/2)( t1 - 6 )2

The answer at the back of the book is 22.7 s
That is not the answer I get when I solve for this.
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
1K
  • · Replies 6 ·
Replies
6
Views
17K
  • · Replies 6 ·
Replies
6
Views
3K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
3K
Replies
8
Views
9K
  • · Replies 30 ·
2
Replies
30
Views
3K
Replies
18
Views
2K
  • · Replies 34 ·
2
Replies
34
Views
3K