2 cars are in a race the first car is 200m ahead of the second car.the first car is moving with a uniform velocity of 30m/s while the second car starts from rest and accelerate to a rate of 4m/s how far and how long will it take the second car to meet the first car

Write equtions for distance travelled vs time for each car. Set them equal and solve for t.

Use that value of t in either X(t) equation to get the location.

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To find out how far and how long it will take for the second car to meet the first car, we need to determine when the two cars are at the same position.

Let's denote the distance traveled by the first car as D1 and the distance traveled by the second car as D2.

The first car is moving with a uniform velocity of 30 m/s. The time taken by the first car to travel a distance D1 can be found using the formula:
t1 = D1 / V1

The second car starts from rest and accelerates at a rate of 4 m/s^2. The distance traveled by the second car can be determined using the equation of motion:
D2 = (1/2) * a * t2^2

Since the second car starts from rest, its initial velocity (u) is 0 m/s. Using the equation of motion:
D1 = u * t2 + (1/2) * a * t2^2

Substituting the values:
D1 = 0 * t2 + (1/2) * 4 * t2^2
D1 = 2t2^2

Now, we know that the first car is initially 200 m ahead of the second car:
D1 = D2 + 200

Substituting the value of D1 from above:
2t2^2 = D2 + 200

Simplifying the equation, we have:
2t2^2 - D2 = 200

Since we have two variables (D2 and t2), we need another equation to solve for both. For this, we can use the equation of motion that relates final velocity (v), initial velocity (u), acceleration (a), and time (t):
v = u + at

Since the second car starts from rest, the equation becomes:
v2 = 0 + 4t2

Now, let's combine this equation with the previous equation to solve for D2 and t2.

2t2^2 - D2 = 200 ... Equation 1
v2 = 4t2 ... Equation 2

To find t2 and subsequently D2, we need to solve these two equations simultaneously.