A car starts from rest and accelerates uniformly at 3.0 m/s2 toward the north. a second car starts from rest 6.0 s later at the same point and accelerates uniformly at 5.0 m/s2 toward the north. how long after the second car starts does it overtake the first car?

To begin, you would need to find the displacement of the first car and the equation to find that is d = 1/2at^2. So you would plug in what you have from the problem into the equation: d = (1/2)3(6)^2 and d is equal to 54 m. THIS IS YOUR DISPLACEMENT FOR THE FIRST CAR.

Next, you need to find the velocity of the car and the equation would be v = at. Plug in what you know from the problem: v = 3(6) which is 18. THIS IS YOUR INITIAL VELOCITY.

Next, we need to find out the distance of the 2nd car and we would use d = 1/2at^2. Plug in what you now from the problem: d = (1/2)5t^2 which would be d = 2.5t^2.

Next, you would equal these two equations together: 2.5t^2 = 1.5t^2 + 18t +54. All these values are from when we solved them from above, and once you solve it you will get 20.625. (SOLVE FOR T)

maheshpatelvVT maheshpatelvVT · Answer 2 · 2022-04-30T19:25:36+02:00

After 20.619 seconds car starts and it will overtake the first car if the car starts from rest and accelerates uniformly at 3.0 m/s^2 toward the north.

What is acceleration?

It is defined as the rate of change in the velocity of a physical particle. It is a vector quantity that has a magnitude as well as direction.

We have:

Acceleration of the first car = 3.0 m/s² toward the north.

Acceleration of the second car = 5.0 m/s² towards the north after 6 seconds from the rest.

Let's suppose the time t represents the first car starts, and t' represents the time for the second car has started.

From the question:

t' = t - 6

For the first car,

[tex]\rm x(t) = \frac{3}{2} t^2[/tex]

For the second car,

[tex]\rm x(t)= \frac{5}{2} (t-6)^2[/tex]

Equate both equations, we get

[tex]\rm \frac{3}{2} t^2= \frac{5}{2} (t-6)^2\\\\\rm 3t^2= 5t^2+180-60t\\\\\rm 2t^2-60t+180= 0[/tex]

After solving the above quadratic equation, we get:

t = 26.619 or

t = 3.38(not taking this one since the second car starts from the rest 6.0s)

Now t' = t - 6 ⇒ 26.619 - 6 ⇒ 20.619

Thus, after 20.619 seconds car starts and it will overtake the first car if the car starts from rest and accelerates uniformly at 3.0 m/s^2 toward the north.

Learn more about the acceleration here:
https://brainly.com/question/12550364