Kinematics

### Average Speed

The motion of a car, which moves with constant speed, is described by the following table

 t (h) 1 2 4 7 9 11 12 S (km) 100 200 450 600 400 200 100

from the table data find:
a) The average speed of the car between the instants 1 h and 2 h;
b) The average speed of the car between the instants 4 h and 7 h;
c) The average speed of the car between the instants 9 h and 12 h;
d) The average speed of the car between the instants 1 and 12 h.
The largest known star (until June 2019) is VY Canis Majoris in the constellation of Canis Major with an estimated diameter of 1,975,000,000 km. Making the (absurd) assumption that a commercial jet could fly close to the surface of the star at a constant speed of 990 km / h, how long would the jet take for a spin on the star, give the answer in years.
A worker leaves his house and walks for 600 meters in 5 minutes to the bus stop, as soon as he reaches the bus stop he takes the bus and travels for 40 minutes at a constant speed of 18 kilometers per hour to the factory where he works. If he took the entire bike route at a constant speed of 6 meters per second how long would it take from home to the factory? Give the answer in minutes.

### One-Dimensional Motion with Constant Speed

The motion of a body is described by the displacement as a function of time

S = − 10 + 4 t

where the position is measured in kilometers and the time in hours. Find:
a) The initial position;
b) The speed;
c) The instant in which the body passes through the origin;
d) The position of the body at time 4 h;
A motorcyclist moves in the opposite direstion of a oriented frame of reference, the speed is 40 m/s and initially his position is -150 m. Find:
a) The equation of displacement as a function of time;
b) In what time it passes the origin.
A high-speed train with a constant speed of 234 km/h runs through a 620 m long tunnel, the train's length is 160 m. What is the time interval to cross the tunnel?
Two boats depart from the same point and travel on the same straight line, with constant speeds of 25 km/h and 35 km/h. Communication between the two boats is possible by radio as long as the distance between them does not exceed 600 km. Find the time interval during which the two boats can communicate, in the following cases:
a) the two boats move in the same direction;
b) the slower boat departs two hours before the other and moves in the same direction;
c) The two boats depart at the same time and move in opposite directions. During a fog, a navigator receives two signals simultaneously sent by a station on the coast, one through the air and the other through the water. Between the receptions of the two sounds, a time interval ?t=5 seconds elapses. Under the conditions of the experiment, the speed of sound in the air is 341 m/s and 1504 m/s in the water. Find the distance x between the boat and the station emitting the signals.

### Average Accelaration

The table below describes the velocities of a particle, it moves in a given reference frame.

 t (2) 0 1 2 3 4 5 6 v (m/s) 9 6 3 0 -3 -6 -9

from the table find:
a) The initial speed of the particle;
;b) The instant when the particle changes its direction;
c) The average acceleration of the particle between the instants 1 s and 2 s;
d) The average acceleration of the particle between the instants 5 s and 6 s;

### One-Dimensional Motion with Constant Acceleration

A motorcyclist is moving in the opposite direction of a reference frame, its initial speed is 25 m/s and at the initial time its position is -150 m, the motorcycle decelerates 2 m/s2. Find:
a) The equation of displacement as a function of time;
b) The equation of velocity as a function of time;
c) The instant in which it passes through the origin of the reference frame;
d) The instant that its speed is zero.
A car moves along a straight road with a speed of 200 km/h. When this car overtake another car, initially at rest at a gas station, it begins to move with constant acceleration 4,5 m/s2 until it reaches the speed of 200 km/h. Find:
a) What is the time elapsed until the car leaving the gas station reaches the speed of 200 km/h?
b) How far are they from each other when their speeds are equal.