Unit 1
Physics and Chemistry
Kinematics
EXERCISES
Average speed
∆𝑠 𝑠𝑓 − 𝑠0
=
∆𝑡 𝑡𝑓 − 𝑡0
1. A girl rides a bike and travels 4 km in 10 minutes. Calculate its average speed in m∙s-1 and km∙h-1.
2. Anna needs 40 minutes to arrive to her high school, which is 2.8 km away from her home. She
stays at school for 7 hours and then comes back home walking for three quarters of an hour. Plot the
graph space vs time and speed vs time, calculating her speed in each phase.
3. A car travels at 75 km∙h-1 through a road. Calculate the time needed to cover a distance of 130 km.
Express the speed in m∙s-1 and calculate the distance travelled in 20 minutes.
4. Order these velocities from the slowest to the highest:
a) 72 km/h
b) 1200 km/day
c) 3563 dm/min
d) 30 m/min e) 15 cm/s
5. Which of these animals is the fastest? Which one is the slowest?
Sloth bear: 0´2 km/h snail: 5000 cm/h
turtle: 70 m/h
6. Speed limits in UK are 30, 50 and 70 miles per hour. Convert these limits in km∙h-1 and m∙s-1.
Use conversion factors. [1 mile=1609 metres]
𝑣=
7. The position of a body throughout time is shown in the following table:
Time (s)
0
1
2
3
4
5
Position (m)
0
2
6
11
14
19
a) Plot the graph position vs time.
b) Calculate the average speed in the intervals from 0 to 1 s, from 0 to 2 s, from 1 to 4 s and from 0
to 5 seconds.
Average acceleration
∆𝑣 𝑣𝑓 − 𝑣0
=
∆𝑡
𝑡𝑓 − 𝑡0
8. A woman travels in her car at 90 km∙h-1 and she accelerates to 120 km∙h-1 in 4 seconds. Calculate
her acceleration in m∙s-2.
9. A car moves in the city with a speed of 50 km/h. When it reaches a red light, it slows down until
it stops. It takes 1 second to stop. What is the acceleration of this car?
𝑎=
Uniform Linear Motion (ULM)
𝑣 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑎=0
𝑠𝑓 = 𝑠0 + 𝑣 ∙ ∆𝑡
10. The distance from Madrid to Córdoba is 401 km. If you travel to Córdoba from Valdemoro
(which is located between Madrid and Córdoba at a distance of 28 km from Madrid), with a
constant speed of 90 km/h, calculate the time you need to arrive there.
11. Andrew starts walking from home to school at a medium velocity of 6 m/s. If the school is 900
m away, how long will it take him to get there?
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Unit 1
Physics and Chemistry
Kinematics
12. A cyclist is in the 25th km of a section that is formed of 115 km. How long will it take him to
reach the end if he cycles at 30 km/h speed?
13. A body has a uniform linear motion with a speed of 8 m/s. Complete the following table and
draw the graph space vs time:
t (s)
0
1
2
3
4
5
s (m)
14. A bird flies at a speed of 15 m/s. Make a table with the position of the bird every 5 seconds for
the first 40 seconds. Draw the graph of displacement versus time using the table you have made.
15. Describe the type of motion in each of the parts of the graphic:
16. Describe the type of motion in each of the parts of the graphic:
17. A car leaves town A at 4 p.m. and arrives to town B, where it stops, at 5.45 pm. At 6.45 p.m., the
car continues the trip and arrives to town C at 8.15 p.m. If the distance between A and B is 189 km,
and between B and C is 135 km, calculate the medium velocity: a) in the trip from A to B; b) in the
trip from B to C; c) in the whole trip. Express the solution in SI units.
Linear Uniform Accelerated Motion (LUAM)
𝑎 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝑣𝑓 = 𝑣0 + 𝑎 ∙ ∆𝑡
1
𝑣𝑓2 = 𝑣02 + 2 ∙ 𝑎 ∙ ∆𝑠
𝑠𝑓 = 𝑠0 + 𝑣0 ∙ ∆𝑡 + ∙ 𝑎 ∙ ∆𝑡 2
2
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Unit 1
Physics and Chemistry
Kinematics
18. Find the constant acceleration needed to allow a car to accelerate in a straight line from a speed
of zero to a speed of 30 m/s in 5 s.
19. An airplane must reach a takeoff speed of 80 m/s in a 1000 m long runway. What minimum
constant acceleration is required?
20. A body starting from rest acquires a velocity of 200 m/s in 10 seconds. Calculate the
acceleration and the distance travelled by the body in 10 seconds.
21. A body starts moving with a velocity of 40 m/s and an acceleration of 10 m/s2. Find the distance
travelled by the body in 15 seconds and the velocity at the end of the 15th second.
22. A driver who is moving at 20 m∙s-1 notices a huge rock on the road, and it takes him 4 seconds
to stop his car. Calculate the acceleration and the distance travelled. If the rock was located at a
distance of 45 m when he saw it, did he have time to avoid crashing the rock?
23. A car increases its speed from 60 km/h to 80 km/h in 6 seconds. Calculate its acceleration, the
speed it will have 9 seconds after starting accelerating and the distance it will have travelled in the 9
seconds (suppose the acceleration remains constant).
24. When approaching the station, a train which initially moved at 110 km/h slows down until it
stops. If the acceleration was -1.5 m/s2, how long did it take the train to stop? What was the distance
from the station when the train began to slow down?
25. A body at rest starts moving with an acceleration of 3 m/s2. Complete the following tables and
plot the graphs space vs time and speed vs time:
Time (s)
0
1
2
3
4
5
0
1
2
3
4
5
Speed (m/s)
Time (s)
Space (m)
26. A body with an initial speed of 1 m∙s-1 accelerates 2 m∙s-1 each second. Draw the graphs space
vs time and speed vs time for the first 8 seconds.
27. A body which moves with a speed of 20 m/s slows down with an acceleration of -2.5 m∙s-2. Plot
the graphs space vs time and speed vs time for every second until it stops.
“Catch up with” exercises
28. A car moves at 120 km/h. Another car, located 3 km ahead, moves at 80 km/h in the same
direction as the first car. When will the first car catch up with the second car? How long will it take
the first car to catch up with the second car? Draw one graph space-time with the motion of the two
cars.
29. A car travels at 85 km/h. Another car, located 8 km ahead, moves at 100 km/h but in opposite
direction, towards the first car. Calculate when will these cars meet and how long will it take them
to meet. Draw one graph space versus time with the motion of the two cars.
30. Two trains are located 2000 m apart. Train one is moving with a constant speed of 30 m/s
directly towards train 2 which starts from rest and accelerates with a constant acceleration of 5 m/s2
directly towards train 1. When will the trains meet?
31. When a traffic light turns green, a car crosses it with a constant speed of 40 km/h. Two seconds
later, another car that was at rest at the traffic light starts moving with an acceleration of 2 m/s2.
When will the second car catch up with the first car? What will be the distance from the street light
then?
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Unit 1
Physics and Chemistry
Kinematics
32. Carlos, who is in Pinto, starts driving to Getafe with a constant speed of 70 km/h. At the same
time, Sandra, who is in Getafe, starts driving to Pinto with a constant speed of 80 km/h. When will
they meet? Where? The distance between Getafe and Pinto is 12.8 km. Take the reference frame in
Pinto.
Free fall motion
33. A body is vertically thrown up from the floor with an initial speed of 25 m/s. Calculate:
a) The time it will need to reach the maximum height.
b) The maximum height.
c) The time it will need to reach the ground again.
d) The speed at which it will reach the ground.
34. You drop an object from an initial height of 10 m. Calculate the time it takes to strike the ground.
35. An object is dropped from a height of 75 m. Calculate the position and the speed of the object 2
seconds later.
36. An apple is vertically thrown down with a speed of 4 m/s from the top of a building which is
101 m high. Calculate the time it will take for the apple to reach the ground and the velocity it will
have at that moment.
37. A ball is dropped from a height of 100 m above ground level. Neglect the effects of air
resistance.
a) What is the velocity of the ball one second after it has been dropped?
b) How long will it take the ball to strike the ground?
c) What is the velocity of the ball when it strikes the ground?
38. A ball thrown straight up in the air reaches a height of 30 m above the level from which it was
thrown. What was the velocity of the ball when it left the hand of the thrower? What was the
velocity of the ball 1.5 seconds after it was thrown?
39. A flower pot falls from a balcony which has a height of 20 metres. Calculate when it will strike
the ground and its velocity then.
40. From a height of 4 metres a ball is thrown vertically up with a speed of 6 m/s. Calculate:
a) The maximum height.
b) The speed when it strikes the ground.
41. A coin is dropped in a well and it reaches the bottom in 4 seconds. Calculate the depth of the
well.
Uniform Circular Motion (UCM)
𝜃 = 𝜃0 + 𝜔 ∙ ∆𝑡
𝑎𝑐 =
𝑣2
𝑅
∆𝑠 = ∆𝜃 ∙ 𝑅
= 𝜔2 ∙ 𝑅
𝑣 =𝜔∙𝑅
𝜔 = 2𝜋𝑓 =
2𝜋
𝑇
42. A cyclist moves with a constant speed of 15 m/s on a circular track whose radius is 50 m.
Calculate:
a) Its angular speed in rad/s and in rpm.
b) The angle the cyclist will have covered in 45 seconds.
c) The distance the cyclist will have travelled in 45 seconds.
d) The centripetal acceleration.
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Unit 1
Physics and Chemistry
Kinematics
43. A body moves with a circular motion with an angular speed of 30 rpm. The radius of the
circumference that is described is 40 cm. Calculate:
a) The angular speed in rad/s.
b) The linear speed in m/s.
c) The linear speed in km/h.
d) The distance the body will have travelled in 1 minute.
e) The centripetal acceleration of the body.
44. A disc whose diameter is 25 cm rotates at 20 rpm. Calculate:
a) Its period and frequency.
b) The linear speed of a peripheral point.
45. The satellite Europa rotates around Jupiter with an average speed of 13740 km/s. The average
distance between the center of Europa and the center of Jupiter is 670900 km. Calculate:
a) The angular speed of this motion in rad/s.
b) The period and the frequency of this motion.
46. The period of the Earth orbiting the Sun is 365.25 days (this 0.25 is the reason there is a leap
year every four years). If the linear speed of the Earth around the Sun is 29.78 km/s, calculate the
average distance between the center of the Sun and the center of the Earth.
47. In a circular motion, a body that rotates an angle of 2.1 rad in 0.25 seconds travels a distance of
6 metres. What is the radius of the circumference? What is the linear speed?
48. The frequency of a disc is 1.2 Hz and its diameter is 45 cm. Calculate its angular and linear
speed and the angle it will have rotated in 2 minutes.
49. The angular speed of a circular motion, whose diameter is 15 m, is 2 rpm. Calculate:
a) The angular speed in rad/s.
b) The linear speed in m/s and in cm/min.
c) The angle, in rad, the body will have rotated in 3.7 minutes.
50. The distance between the Moon and the Earth is 384000 km and the time the Moon needs to
complete a revolution around the Earth is 29.5 days. Calculate the angular speed and the linear
speed of the Moon.
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