Physics 1
2 – Kinematics – 1D motion and free fall
Exercise 1.
The runner ran half of the distance with the speed v1 = 18 [km/h] and the second half of the distance
with unknown speed v2. If he would ran whole time with the constant speed
v = 12 [km/h] then the time required for traveling the whole distance would not change. What should
be v2 speed?
Exercise 2.
A subway train starts from rest at a station and accelerates at a rate of 1.6 [m/s2] for 14 [s]. It runs at
constant speed for 70 [s] and slows down at a rate of 3.5 [m/s2] until it stops at the next station. Find
the total distance covered.
Exercise 3.
A train starts from rest at station A and accelerates at 0.5 [m/s2] for 60 [s]. Afterwards it travels with
a constant velocity for 15 [min]. It then decelerates at 1 [m/s2] until it is brought to rest at station B.
Determine the distance between the stations.
Exercise 4.
When two cars A and B are next to one another, they are traveling in the same direction with speeds
vA and vB, respectively. If B maintains its constant speed, while A begins to decelerate at aA,
determine the distance d between the cars at the instant A stops.
Exercise 5.
With what speed must a ball be thrown vertically from the ground level to rise to a maximum height
of 50 [m]? How long will it be in the air?
Exercise 6.
A ball is thrown directly downward with an initial speed of 8 [m/s] from a height of 30 [m]. When
does the ball strike the ground?
Exercise 7.
A student throws a set of keys vertically upward to her sister in a window 4 [m] above. The keys are
caught 1.5 [s] later by the sister’s outstretched hand. With what initial velocity were the keys thrown?
What was the velocity of the keys just before they were caught?
Exercise 8.
A falling object requires 1.5 [s] to travel the last 30 [m] before hitting the ground. From what height
above the ground did it fall?
Exercise 9.
A stone falls from rest from the top of a high cliff. A second stone is thrown downward from the same
height 2 [s] later with an initial speed of 30 [m/s]. If both stones hit the ground simultaneously, how
high is the cliff?
Exercise 10.
The rocket is fired from the launch pad starting from rest but with constant acceleration of
3.5 [m/s2] upward. At 25 [s] after launch, the second stage fires for 10 [s], which boosts the rocket’s
velocity to 132.5 [m/s] upward at 35 [s] after launch. After the second stage has finished firing, the
only force acting on the rocket is gravity (air resistance can be neglected). Find the maximum height
that the stage–two rocket reaches above launch pad. How much time after the end of stage–two firing
will it take for the rocket to fall back to the launch pad? How fast will the stage–two rocket be moving
as it reaches launch pad?