Two cars driving toward each other (non-uniform speed)

In summary, when the two cars are 1.4 km apart and travelling towards each other, the car that starts from rest will meet the other car 36 seconds after starting.
  • #1
Stormblessed
24
2

Homework Statement



Two cars are 1.4 km apart and driving towards each other. One car starts from rest and accelerates uniformly at 1.2 m/s^2. The other car is driving at a constant speed of 18 m/s. When will the cars meet?

Homework Equations



d=vt
d=ut + 1/2at^2
d=vt-1/2at^2
v^2 = u^2 + 2ad

Note: u is initial velocity and v is final velocity

The Attempt at a Solution



The answer provided by the teacher is 36 seconds. I don't know how to get there. I understand what to do if both cars have constant speed (create two equations equal to each other and solve for time) but I don't know what to do if one car is accelerating. If I use the algebraic method, I am getting 30 s instead of 36 s.

d1 = 1/2at^2
d1 = 1/2(1.2)t^2
d1 = 0.6t^2

d2 = vt
d2 = 18t

d1 = d2
0.6t^2 = 18 t
t = 30 s (which is incorrect)
 
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  • #2
Stormblessed said:
d1 = d2
Why does each car have to travel the same distance?

Think about what d1 + d2 should equal.
 
  • #3
TSny said:
Why does each car have to travel the same distance?

Think about what d1 + d2 should equal.
Oh, so can the equation be written as:

0.6t^2 + 18 t = 1400

And then I just solve for t?
 
  • #4
Give it a try.
 
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  • #5
TSny said:
Give it a try.

Ok, this works (t = 35.5). Thanks a lot. So does this apply (d1 + d2 = dtotal) for all "two cars driving toward each other" questions?
 
  • #6
Yes. So, when both cars travel with constant velocity, you would still set up d1 + d2 = initial separation distance.

However, there is another way to think about it. Introduce an x-axis and let the position of the cars on the axis be x1 and x2. Set up equations for x1 and x2 as functions of time. Then you would be looking for the time when x1 = x2.

The difference in these two approaches is that x represents position on the x-axis, whereas d represents distance traveled.
 
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Related to Two cars driving toward each other (non-uniform speed)

1. What is the distance between the two cars when they start driving toward each other?

The distance between the two cars when they start driving toward each other depends on their starting positions and the direction they are driving in. If they are both starting from the same point, the distance between them would be zero. If they are starting from different points, the distance would be the difference between their starting positions.

2. How do you calculate the time it takes for the two cars to collide?

The time it takes for the two cars to collide can be calculated by dividing the distance between them by the sum of their speeds. This is based on the formula d = rt, where d is the distance, r is the rate (or speed), and t is the time.

3. What happens if the cars have different speeds?

If the cars have different speeds, they will eventually collide with each other. The car with the higher speed will catch up to the slower car and they will both continue to travel at the same speed until they collide. The time it takes for them to collide will depend on their speeds and the distance between them.

4. Can the cars collide if they are traveling in opposite directions?

Yes, the cars can still collide if they are traveling in opposite directions. This is because they are still moving towards each other, just in different directions. The time it takes for them to collide will be shorter compared to if they were traveling in the same direction.

5. What factors can affect the outcome of the collision between the two cars?

The outcome of the collision between the two cars can be affected by various factors such as the speeds of the cars, their masses, and the angle at which they collide. These factors can determine the force of impact and the severity of the collision. Other factors like weather conditions and road conditions can also play a role in the outcome of the collision.

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