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14 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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Tutorial
-
Kinematics


BTE1013



1.

A train travels 50 km in half an hour. It then stops at a station fro

20 minutes,
before travelling for 2 hours at an average speed of 90 km/h. What was the
train’s average speed over the whole journey?

2.

A car starts from rest and reaches a velocity of 100 kn/h after accelerating
uniformly for 10s. What distance has it trave
lled? What was its average
velocity?

3.

A train travels a distance
s

in a straight line. For the first half of the distance its
velocity has the constant value v
1
, and for the second half it has the constant
value v
2
. What is the average velocity? Is it large

or smaller than (v
1

+ v
2
)/2?

4.

A police officer on a motorcycle chases a speeding car on a straight highway.
The car’s speed is constant at v
c

= 120 km/h, and the officer is a distance
d

=
500 m behind it when she starts the chase with velocity v
p

= 180 km/
h. What
is the police officer’s speed relative to the car? How long will it take her to
catch up with it?

5.

Taking off from a point on the Equator in the late afternoon and flying due
West, passengers on the Concorde supersonic airliner see the sun set and
t
hen rise again ahead of them. Estimate Concorde’s minimum speed. (Earth’s
radius = 6400 km).

6.

The maximum straight
-
line deceleration of a racing car under braking is 5 m
s
-
2
. What is the minimum stopping distance of the car from a velocity of 100
km/h? Wha
t does this distance become if the velocity has twice this value?

7.

A rocket
-
powered sled accelerates from rest. After
t

= 10 s it has travelled a
distance
x

= 400 m. What is its speed in km/h at this point?

8.

A ball is thrown vertically upwards with initial s
peed 10 ms
-
1

from the edge of
a roof of height
H

= 20 m. How long does it take for the ball to hit the ground?
At what velocity does it hit the ground?

9.

A stone is dropped from rest into a well. It is observed to hit the water after 2
s. Find the distance down to the water surface. How fats must the stone be
thrown downwards in order to hit the surface after only 1 s? What are the
impact velocities in the
two cases?

10.

A car and a truck start moving at the ame time, but the truck starts some
distance ahead. The car and the truck move with constant accelerations a
1

=2
ms
-
2
, a
2

= 1 ms
-
2

respectively. The car overtakes the truck after the latter has
moved 32 m. H
ow long did it take the car to catch up with the truck? What
were the velocities of the velocities of the car and the truck at that moment?
How far apart did the truck and the car start?

11.

A rocket climbs vertically and is powered in such a way t
h
at it has c
onstant
acceleration
a
. It reaches a height of 1 km with a velocity of 100 ms
-
1
. What is
the value of
a?
How long does the rocket

take to reach this 1 km height?

Tutorial
-
Kinematics


BTE1013



12.

A bullet is fired vertically from a toy pistol with muzzle velocity 30 ms
-
1
. How
high above th
e firing point does the bullet go before falling back under
gravity? What is its velocity 4s after being fired? At height is it then?

13.

A body falls freely from rest to the ground a distance
h
below. In the last 1 s of
its flight it falls a distance
h/
2. Wha
t is
h
?

14.

A man falls from rest from the top of a building of height
H

= 100 m. A time
t

=
1 s later, Superwoman swoops after him with initial speed v
o

downwards,
subsequently falling freely. She catches the man at a height
h
= 20 m above
the ground. What was v
o
?

15.

A boy in an elevator throws a ball vertically upwards with speed v
o

= 5 m s
-
2

relative to the elevator. The elevator has constant upward acceleration
a
= 2
m s
-
2
. How long does it take for the ball return to the boy’s
hand?


















Tutorial
-
Kinematics


BTE1013



Solution no. 34


no. 48 refer to the question no. 1


no. 15.


Tutorial
-
Kinematics


BTE1013




Tutorial
-
Kinematics


BTE1013




Tutorial
-
Kinematics


BTE1013