A race car starts from rest on a circular track. The car increases its speed at a constant rate at as it goes 4.25 times around the track. Find the angle that the total acceleration of the car makes with the radius connecting the center of the track and the car at the moment the car completes its trip of 4.25 times around the circle.

Angle = 1.07°

Explanation:

Total acceleration consists of translational acceleration (a) which is tangential and centripetal acceleration which is (radial).

Now, Tangential and radial acceleration are always perpendicular to each other. Thus, in a triangle system they are opposite and adjacent sides. From trigonometric ratios,

Opposite/Adjacent = tanθ

Now centripetal acceleration is given as v²/r

Thus, the angle to the radial is given as;

tanθ = translational acceleration/centripetal acceleration

So, tanθ = a/(v²/r) = ar/v²

Thus, θ = tan^(-1)(ar/v²)

Now, Distance of one round of circular motion of 'r' radius

= circumference of circle = 2πr

N = number of trips car makes around the circle

Thus,

total distance = 2πrN

Now, from equation of motion, we know that v² = u² + 2as

Where s is total distance and u is initial velocity which is zero in this case.

Thus, v² = 0² + 2as

Making s the subject;

s = v²/2a

Thus,

2πrN = v²/2a

So let's simplify to bring out ar/v² which is what we will use to calculate the angle. So,

2πrN x 2a = v²

4πN(ar) = v²

Thus, ar/v² = 1/(4πN)

From the question, N = 4.25

Thus,

ar/v² = 1/(4π x 4.25) = 0.0187

From earlier, we saw that the angle is given by;

θ = tan^(-1)(ar/v²)

Thus, θ = tan^(-1)(0.0187)

θ = 1.07°

an obstruction

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.