Kinematics -motion in a straight line | year 2024-2025

Recitation 2

Exercises * are mandatory

Multiple-choice question (MCQ)*
1. A point M describes a straight trajectory.
A. Its speed is constant
B. Its velocity vector is constant
C. Its acceleration-velocity vector is constant.
D. Its acceleration vector is collinear with the velocity vector.
E. Its acceleration vector is orthogonal to the velocity vector.
2. The area under a velocity-time graph (v=f(t)) represents:
A. acceleration
B. the variation of acceleration
C. speed
D. variation of speed
E. the displacement
3. Which of these graphs represents the motion of an object moving with a constant non-zero speed?

4. An object is falling in free fall without initial velocity. Which of these graphs correctly represents the
motion?

5. The
diagram represents the rectilinear motion of a car. Which of the following statements is correct?

A. The car accelerates, stops and reverses

B. The car accelerates at 6 m/s 2 for the first 2 s
C. The car is rolling for a total time of 12 s
D. The car decelerates by 12 m/s 2 during the last 4 s
E. The car returns to its starting point when t = 9 s
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Kinematics -motion in a straight line | year 2024-2025

6. Which of the following five graphs of acceleration versus time is correct for an object moving in a straight
line at a constant speed?

7. Two
balls of different masses ( m1 = 0.8kg and m2 = 1.2kg ), initially at rest, fall into a vacuum from the same
height h .
Which ball hits the ground first?
A. Both balls hit the ground at the same time.
B. The ball of mass m 1
C. The ball of mass m 2
Gggvf
Exercice1:
A particle M undergoes rectilinear motion along an axis (x'ox). The figure below shows its displacement
diagram. V(t).
x(m) 2
1. Describe 3. Determine the 1
qualitatively the nature of the motion 0
motion of the mobile in different phases. -1
along the x'ox axis. 4. Using the
2. Represent the displacement 246
velocity diagram diagram, calculate 8 10
the t(s)
distance traveled between t=0s and t=10s. What
does this distance correspond to on the V(t) graph?

Exercice2 *:
A particle moves along a straight line ( Ox axis) with an acceleration a = 6t - 8.
1. Find the velocity v(t) and the position x(t) of the particle, knowing that at t = 0, v(0) = 5 m/s and x(0)
= 1 m.
2. Determine the time intervals during which the particle is moving in the positive x-direction and
those in which it is moving in the negative x-direction.
3. Indicate when the motion is accelerated or decelerated.

Exercise 3*:
The figure opposite shows the velocity diagram of an object
undergoing rectilinear motion as shown at t = 0 t=10s. 1
and x=0 . 3 2. Determine the nature of the motion in each
1. Draw the acceleration and displacement phase.
diagrams

2
(position-time graph) between the instants t=0 and
3. Calculate the distance traveled between t=0 and
t=10s. -1
4. On the trajectory, represent the position,
velocity, and -2
acceleration vectors at t = 8s. 2 4 6 8 10
Scale: 1cm → 1m; 1cm → 1m/s; 1cm → 1m/s².

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Kinematics -motion in a straight line | year 2024-2025
3. Calculate the total distance covered by the
Exercise 4*:
The velocity diagram of a particle undergoing particle. Exercise 5:
straight motion is provided in the graph opposite.
At t=0s, x=1m.

V(m/s)
2
1. Identify the phases of the motion. Justify your t(s)
10 20 30 40
answer. ggg
2. Find the equations of motion for each phase.
2

-2
The figure opposite depictst=30s, with v(0)=15m/s.
the acceleration diagram of2. On the trajectory, draw
a particle undergoing the position, velocity, and
rectilinear motion a(m/s
) 10 20 30 0
1. Plot the velocity graph t(s)
V(t) between t=0s and
acceleration vectors at t1=5s and t2=15s, given that at t=0s,
-1
x=0m. Scales: 4cm → 50m; 2cm → 5m/s; 1cm → 1m/s².
Exercise 6*:
A ball is thrown upward with an initial velocity of 20 m/s from the top of a 50 m high rock. When it falls
back down, it narrowly misses the rock. Neglecting air resistance, calculate the following: 1. tA the
moment when the ball passes the top of the rock, and the speed VA at this moment? 2. t B the moment
when the ball hits the ground, and the speed V B at that moment 3. The maximum height L max reached by
the ball from the ground?
4. The speed (v) needed to throw the ball upward so that it hits the ground 3 seconds after passing the
top of the rock.

Exercise 7:
A train, upon departing from the station, is subjected to a constant acceleration a. It enters a tunnel with a
velocity v1 and covers a distance of 24 m during the first two seconds, then 32 m during the following two
seconds.
1. te a.
Calcula vet 1
The acceleration is removed 10 seconds after departure. The train then travels at a constant speed for
30 s, after which it experiences a constant deceleration with a value of a'=-2 m/s2 until it comes to a
stop at the next station.
2. Plot velocity diagram, v(t), of the train and calculate the distance between the two stations.

Exercise 8*
A car A is stopped at a red traffic light at a distance of d1=3m. When the light turns green, A starts with a
constant acceleration a1=3m/s². At the same time, another car B, traveling at a constant speed V2=54km/h, is
located at a distance of d2=24m from the traffic light (o) (see the figure below).

1. Find the time equations xA(t) and xB(t) for cars A and B, respectively.
2. Determine the times of overtaking of A and B, and the position which corresponds to this overtaking.

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Kinematics -motion in a straight line | year 2024-2025

3. If car B were traveling at the speed V2=36km/h, could it catch up with car A? If not, then find the
time when the distance between the two cars is minimal and calculate this distance.
light turns green, A starts constant Va
Exercise 9 moving. At the same 100 75 Vb
A car A is stopped at a time, another car B 50
t(s)
red traffic light. When the overtakes A, traveling at a V(Km/h)
speed. The velocity diagrams are represented in 3.6 7.2 10.8 0
the figure below.

1. How much time did car A take to reach the same speed as car B?
2. At that moment, how far is car A from car B?
3. Which car is in the lead (first) and by how much at t = 5.4s and t = 10.8s?
4. At what moment does car A catch up to car B?

Exercise 10
A material point moves on the OX axis. The relationship between its speed v and its abscissa x
is: ��2 = ���� + �� where A and B are constants.
1. Calculate the acceleration of the mobile. What can we say about the movement? 2. Knowing the
nature of the movement, find the values of A and B according to the characteristics of the movement.
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