At t=0 car A and truck B are 350 m apart on a straight road. Starting from rest car A speeds up with a constant acceleration of 10 m/s^2. Truck B is travelling in the opposite direction with a constant speed of 15 m/s. How far away is car A from its starting point when the two vehicles pass each other?
Write equations describing position vs time for both cars separately. Set the positions equal and solve for t. Use that t to compute the location.
Someone here will be glad to critique your work.
To find the distance at which the two vehicles pass each other, we need to determine how long it takes for car A to catch up with truck B.
Let's start by calculating the time it takes for car A to catch up with truck B. We can use the equation of motion:
s = ut + 0.5 * a * t^2
where:
s = distance traveled
u = initial velocity
a = acceleration
t = time
For car A:
u = 0 m/s (starting from rest)
a = 10 m/s^2
s = the distance traveled by car A until it catches up with truck B
Since the distance between the two vehicles is 350m, and they are moving towards each other, their distance will decrease at a rate of (15 m/s + 0 m/s) = 15 m/s. Therefore, the equation becomes:
s = 15t
For car A, using the equation of motion:
350 = 0.5 * 10 * t^2
Now we can solve for t:
350 = 5t^2 (divide both sides by 0.5 * 10)
t^2 = 350/5
t^2 = 70
t = sqrt(70)
Using a calculator, we find that t ≈ 8.37 seconds.
Now let's find the distance traveled by car A during this time.
Using the equation of motion:
s = ut + 0.5 * a * t^2
For car A:
u = 0 m/s (starting from rest)
a = 10 m/s^2
t ≈ 8.37 seconds
s = 0 * 8.37 + 0.5 * 10 * (8.37)^2
s ≈ 0 + 418.5
s ≈ 418.5 meters
Therefore, car A is approximately 418.5 meters away from its starting point when the two vehicles pass each other.