A train is moving parallel and adjacent to a

highway with a constant speed of 30 m/s. Ini-
tially a car is 44 m behind the train, traveling
in the same direction as the train at 42 m/s
and accelerating at 3 m/s2.
What is the speed of the car just as it passes
the train?

Here S=44m

V=42m/s
U=?
a=3m/s²
Now we know that
2as=v²-u²
2(3)(44)=(42)²-u²
u=10√15m/s

38.73

Thanks you

To find the speed of the car just as it passes the train, we need to determine the time it takes for the car to catch up with the train.

Let's start by finding the time it takes for the car to catch up with the train.

First, we can find the relative speed between the car and the train. Since they are both moving in the same direction, we subtract the speed of the train from the speed of the car:

Relative speed = Car's speed - Train's speed
Relative speed = 42 m/s - 30 m/s
Relative speed = 12 m/s

Next, we can determine the distance the car needs to cover to catch up with the train, which is the initial distance between them:

Distance = 44 m

Now, we can use the equation of motion to find the time it takes for the car to catch up with the train:

Distance = (Initial velocity × Time) + (0.5 × Acceleration × Time^2)

Rearranging the equation, we get:

0.5 × Acceleration × Time^2 + (Initial velocity × Time) - Distance = 0

Substituting the values we know:

0.5 × (3 m/s^2) × Time^2 + (42 m/s) × Time - 44 m = 0

Now, we can solve this quadratic equation to find the value of Time.

Using the quadratic formula:

Time = (-b ± √(b^2 - 4ac)) / (2a)

Here, a = 0.5 × (3 m/s^2) = 1.5 m/s^2, b = 42 m/s, and c = -44 m.

Time = (-42 m/s ± √((42 m/s)^2 - 4 × 1.5 m/s^2 × (-44 m))) / (2 × 1.5 m/s^2)

By solving this equation, we get two possible values for Time. However, we discard the negative value since time cannot be negative in this context. So, we only consider the positive value for Time.

Once we find the value of Time, we can substitute it into the equation for the relative speed to find the speed of the car just as it passes the train:

Speed of the car just as it passes the train = Relative speed + Train's speed

By substituting the values we have:

Speed of the car just as it passes the train = 12 m/s + 30 m/s

Calculating this, we find:

Speed of the car just as it passes the train = 42 m/s

Therefore, the speed of the car just as it passes the train is 42 m/s.