Two Cars Colliding: When Do They Meet?

  • Thread starter Thread starter Walan
  • Start date Start date
Click For Summary
SUMMARY

In the discussion, two cars accelerate towards each other from rest, one at 100 m/sec² and the other at 150 m/sec², starting 500 meters apart. The correct approach to determine the time until collision involves using the equation x = (Vo)t + 1/2a(t²) for each car's displacement, where Vo is the initial velocity (0 in this case) and a is the respective acceleration. The total displacement of both cars must equal 500 meters, leading to the equation x + y = 500m. The initial misunderstanding of treating acceleration as velocity was clarified, emphasizing the importance of using the correct kinematic equations.

PREREQUISITES
  • Understanding of kinematic equations, specifically x = (Vo)t + 1/2a(t²)
  • Basic knowledge of acceleration and its units (m/sec²)
  • Familiarity with the concept of relative motion and displacement
  • Ability to solve algebraic equations involving multiple variables
NEXT STEPS
  • Study the derivation and application of kinematic equations in physics
  • Learn about relative motion in one-dimensional systems
  • Explore problems involving constant acceleration and collision scenarios
  • Practice solving algebraic equations with multiple variables in physics contexts
USEFUL FOR

Students studying physics, particularly those focusing on kinematics and motion, as well as educators looking for examples of collision problems involving acceleration.

Walan
Messages
2
Reaction score
0

Homework Statement



Two cars approach each other from opposite directions. One accelerating due east at 100 m/sec^2 and the other accelerating due west at 150 m/sec^2. If they are 500m apart and start from rest, how long does it take for them to collide? Assume constant acceleration.

Homework Equations

. [/B]

The Attempt at a Solution

. [/B]
I can do this with velocities, but am unsure how things change given acceleration. With velocity, one equation was x=100t where x is displacement and t is time, then y=150t where y is displacement and t is also time. The time to impact is the same for each car though the displacement is not. Also, the total displacement of the two cars is 500m so, x + y = 500m
I solved for time and that was that. When I did the same thing with acceleration I got time in sec^2 and knew I had a problem. Would I use the equation x = (Vo)t + 1/2a(t^2) where x is displacement, Vo is initial velocity (which = 0), a is acceleration and t is time? If I used each acceleration in this equation, one displacement x and one displacement y with the total of x + y = 500m would that be right?
 
Physics news on Phys.org
Walan said:

Homework Statement



Two cars approach each other from opposite directions. One accelerating due east at 100 m/sec^2 and the other accelerating due west at 150 m/sec^2. If they are 500m apart and start from rest, how long does it take for them to collide? Assume constant acceleration.

Homework Equations

. [/B]

The Attempt at a Solution

. I can do this with velocities, but am unsure how things change given acceleration. With velocity, one equation was x=100t where x is displacement and t is time, then y=150t where y is displacement and t is also time. The time to impact is the same for each car though the displacement is not. Also, the total displacement of the two cars is 500m so, x + y = 500m
I solved for time and that was that. When I did the same thing with acceleration I got time in sec^2 and knew I had a problem. Would I use the equation x = (Vo)t + 1/2a(t^2) where x is displacement, Vo is initial velocity (which = 0), a is acceleration and t is time? If I used each acceleration in this equation, one displacement x and one displacement y with the total of x + y = 500m would that be right?[/B]

Welcome to PF!
As the cars are accelerating, your first approach is wrong. And the given data, 100m/s^2 and 150 m/s2 are accelerations, not velocities.
The second approach is right, go ahead!
 
Thank you for your help with my question!
 

Similar threads

Oblique soccer shot calculation task
  • · Replies 38 ·
2
Replies
38
Views
4K
Relating acceleration to distance and time
  • · Replies 5 ·
Replies
5
Views
3K
Finding the x component of position vector
  • · Replies 3 ·
Replies
3
Views
835
Would particle P be under non-unform circular motion?
  • · Replies 29 ·
Replies
29
Views
2K
Double Differentiation and Acceleration in a Four Pulley System
  • · Replies 6 ·
Replies
6
Views
2K
Finding velocity for projectile given distances and launch angle
  • · Replies 3 ·
Replies
3
Views
2K
Pushing a stalled car out of an intersection
  • · Replies 1 ·
Replies
1
Views
2K
Solving for Work Done When Accelerating a Mass
  • · Replies 3 ·
Replies
3
Views
936
Projectile motion of a cannon ball versus time
  • · Replies 15 ·
Replies
15
Views
2K
Ball launched from a height of 5 meters --- Projectile motion
  • · Replies 12 ·
Replies
12
Views
1K