Aremote controlled car is moving in a vacant parking lot. the velocity of the car as a function of time is given by v= [5.00 m/s – (0.0180 m/s2)t^2 ]i+[2.00 m/s + (0.550 m/s2)t ]j . what are the magnitude and direction of the velocity of the car at t= 8.00 s?

The magnitude and direction of the velocity of the car at t = 8.00 s is v = 7,468 m / s and the vector direction = θ = 58,984°

In the coordinates of the two-dimensional plane (xy) there is a position vector of a point

You can write P as:

P = xi + yi

where i denotes the unit vector in the x and y directions

While the magnitude of the vector:

and its direction

Likewise with the instantaneous speed which is a derivative of the position function of time

V = vx i + vy j

The velocity of the car as a function of time is given by v = [5.00 m / s - (0.0180 m / s²) t²] i + [2.00 m / s + (0.550 m / s²) t] j so that:

vx = 5 - 0.0180t² i

vy = 2 + 0.55t j

So the instantaneous velocity at t = 8 s becomes:

vx = 5-0.0180.8²

vx = 3,848 m / s

vy = 2+ 0.55.8

vy = 6.4

So the velocity position vector becomes:

v = 3,848 i + 6.4 y

and the magnitude becomes:

v = 7,468 m / s

While the velocity vector direction:

θ = 58,984

Which vector should be negative

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the statements that describe a vector

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the resultant vector

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Keywords: velocity, vector, two-dimensional coordinates,

air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.