Exercises in Physics for the lecture "Physics 1", Electronics and Telecommunications, regular
t winter semester 2010/2011
studies, 1st. year,
Set 2. Kinematics
Motion along a straight line: displacement, average velocity, instantaneous
velocity, average acceleration, instantaneous acceleration, basic equations for
the motion with constant acceleration, free-fall acceleration .Projectile motion.
Uniform circular motion
Ex.1
The position of a particle moving along the x-axis depends on the time according to the
equation:
where x is in meters and t is in seconds.
Find:
1. the average velocity for the time interval (
,
2. the instantaneous velocity at t=1s,
3. the position at t=1s,
4. the displacement ∆x during the first two seconds of the motion,
5. the total distance that the particle moves from the start to t=2s,
6. sketch x versus t and indicate how the answer to question 5 can be obtained from the
graph,
7. what kind of motion does the particle move?
Ex.2
The position of an object moving along the x-axis is given by:
where x is in meters and t is in seconds.
Find:
1. the position of the object at t=1s, t=2s, t=3s, t=4s,
2. the displacement of the object between t=1 and t=4s,
3. the average velocity for the time interval from t=2 to t=4s,
4. the instantaneous velocity at t=1s,
5. the instantaneous acceleration at t=4s,
6. what kind of motion does the particle move?
Ex.3
A car traveling with the velocity v=56 km/h was in the distance s=24m from a barrier when the
driver slammed on the brakes. The car hit the barrier t=2s later.
1. what was the magnitude of the car constant acceleration before the impact?
2. what was the velocity of the car at the impact?
Ex.4
On a dry road, a car with good tires may be able to brake with a constant deceleration
2
a=-4.92 m/s . The car is traveling with the velocity v=24.6 m/s.
1. how long does such a car take to stop?
2. how far does it travel in this time?
3. graph x versus t and v versus t for the deceleration.
Ex.5
2
The brakes on your car can slow you at a rate of 5.2 m/s . If you are going 137 km/h and
suddenly see a radar control , what is the minimum time in which you can get your car under 70
km/h speed limit. Graph x versus t and v versus t for such a slowing.
Ex.6
Water drips from the nozzle of a shower onto the floor of the bathroom 200 cm below. The drops
fall at regular (equal) intervals of time. The first drop is striking the floor at the instant when the
fourth drop begins to fall. Find the position below the nozzle of the second and third drops when
the first drop strikes the floor.
Ex.7
A rock is thrown upward from the ground level at t=0. At t=1.5s it passes the top of a tall
tower, and 1s later it reaches its maximum height. What is the height of the tower?
Ex.8
v0=240
to
the is
horizontal.
is located
at the
height
A ball
launchedThe
fromwindow
the window
with the
initial
h=15
above
the
ground
level.
The
free-fall
acceleration
m/s
velocity
2
g=10m .
m
Find:
/s
1. the components of the position vector
at the angle 3 °
0
of
,
2. the equation of the path
y(x),
3. the
maximum height the ball reaches
H,horizontal range
4. the
5. the
R, components of the velocity vector
,
6. the velocity of the ball at the place where it reaches the horizontal range,
7. the angle between the velocity vector
and the
positive
direction of
the x-axis at
the place
Ex.8
A stone is projected at a cliff of height h with thewhere
initialit speed v =42 m/s and directed at angle
0
reaches the
θ =60° above the horizontal. The stone strikes the
cliff
at
point
A in time t=5.5s after launching.
horizontal
0
range.
Find:
1. the height h of the cliff
2. the speed v of the stone just before impact at A,
k
3. the maximum height H the stone reaches above the ground.
Fig.1. Ex. 8.
Ex.9
A boy whirls a stone in a horizontal circle of radius r=1.5m and at height h=2m above the ground
level. The string breaks and the stone flies off horizontally and strikes the ground after traveling a
horizontal distance R=10m. What is the magnitude of the centripetal acceleration of the stone
during the circular motion?
Ex.10
A particle moves along a circular path over a horizontal xy coordinate system at constant speed.
At time t =4s, it is at point P ( 5, 6) [m] with velocity 3
1
1
[m/s] and acceleration in the positive x
direction. At time t =5s, it has velocity -3
2
[m/s] and acceleration in the positive y direction. What are the x and y coordinates
of the centre of the circular path O(x,y) if t -t is less than 1 period?
2 1