Question

Hello.. I really need help with this Physical question, please, thank you?

Two cars move along the same curve. The hourly equations of each of them are:

Where time is counted from t = 0 and the units are those of S.I.

Will they meet?
Determine the time instant for which the distance between them is minimal (or maximum?).
Determine the speed of the furniture at the instant of time above.
EXERCISE 2

Consider crossing two avenues in a flat part of a city. One of them corresponds to the 0y axis and the other to the 0x axis. A car The traffic at constant speed
in relation to origin 0. Another car B, is at rest at the intersection, waiting for the green light. As A passes through the intersection the signal turns green and car B starts with time dependent speed such that in the first 5 seconds its speed is given by:

After 5 seconds the car B maintains its constant speed. The car A keeps its speed constant all the time. When car B starts moving car A is 10 meters from it. At that moment, we began to count the time. With this data, determine:

The vectors positions of the two cars as a function of time.
The distance between cars A and B as a function of time and their distance after 5 seconds.
The speed of car B in relation to car A, after 5 seconds of the event described.

Answer 1

`"please have a look at the animation below."`

Explanation:

• The cars are symbolized by red and blue dots.
• It is assumed that the cars are moving on the following curve.

`y=1/300 x^2+x+3"(green curve)"`

• The x-coordinates of the car positions do not depend on the function you select.
• The y-coordinate of the car positions depends on the function you select.

• At t = 0 the position of the points is shown on the figure.

`"The red car's position at t = 0:"`
`S_1(0)=-t^4+4t^2=0+0=0`

`"The blue car's position at t = 0:"`
`S_2(0)=-4t^2-9=0-9=-9`

• At t = 3 the cars are in the same point(C) on the curve.

`-t^4+4t^2=-4t^2-9`

`-t^4+8t^2+9=0`

`t=+-3" there is no negative time. "t=3`

• At t = 3 the distance between cars is minimum(zero).

• If t> 3, the distance between the cars increases.