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Published on: 12/08/2019
Motion
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1.
A bus decreases its speed from 80 km \(h^{ -1 }\) to 60 km \(h^{ -1 }\) in 5 s. Find the acceleration of the bus.
2.
Distinguish between speed and velocity.
3.
When is a body said to have
(i) uniform velocity; and
(ii) variable velocity?
4.
What is meant by a point object? Give some examples.
5.
Define the terms rest and motion Give one example for each.
6.
An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?
7.
Define acceleration .Is it a scalar or a vector quantity?
8.
Define the term average speed.
9.
Give two differences between distance and displacement
10.
What is non-uniform motion? Give some examples.
11.
Define speed of body.
12.
What does the odometer of an automobile measure?
13.
On a 100 km track , a train travels the first 30 km at a uniform speed of 30 km \(h^{ -1 }\)How fast must the train travel the next 70 km so as to average 40 km \(h^{ -1 }\) for the entire trip?
14.
In the maximum speed of the marble is
20\(m/s^{ 1 }\)
40 \(m/s^{ 1 }\)
60 \(m/s^{ 1 }\)
80 \(m/s^{ 1 }\)
15.
The distance travelled by a freely falling body is proportional to the
mass of the body
square of the time of fall
square of the acceleration due to gravity
time of fall
16.
The slope of speed-time graph gives
speed
velocity
acceleration
momentum
17.
The initial velocity of a train which is stopped in 20 s by applying brakes retardation due to brakes being 1.5 \(ms^{ -2 }\) is
30 \(ms^{ -2 }\)
30 \(cm^{ -1 }\)
20 \(cm^{ -1 }\)
24 \(ms^{ -1 }\)
18.
The initial velocity of a body is u.It is under uniform acceleration a its velocity v at any time t is given by
\(v=u+at^{ 2 }\)
\(v=u+\frac { 1 }{ 2 } at^{ 2 }\quad \)
v = u + at
v = u
19.
The SI of velocity is
\(ms^{ -1 }\)
\(ms^{ -2 }\)
\(ms^{ -3 }\)
\(Nm^{ -1 }\)
20.
Displacement is a .......... quantity and distance is a ..................... quantity
1.
Initial speed,u = \(80\frac { km }{ h } =\frac { 80X1000m }{ 3800s } =\frac { 800 }{ 36 } ms^{ -1 }\)
Final speed,v = \(60\frac { km }{ h } =\frac { 60X1000m }{ 3800s } =\frac { 600 }{ 36 } ms^{ -1 }\)
Acceleration,u = \(a=\frac { v-u }{ t } =\frac { \frac { 600 }{ 36 } -\frac { 800 }{ 36 } }{ 5 } =\frac { 200 }{ 36X5 } ms^{ -2 }\)
= \(-\frac { 10 }{ 9 } ms^{ -2 }=-1.11ms^{ -2 }\)
2.
Speed of a body needs only magnitude and not direction for its complete description while the velocity needs both magnitude and direction for its complete description so speed is a scalar quantity while velocity is a vector is a vector quantity for example when a car moves wit a speed of 60km/h in the direction 45 degree south of west,we can say that the car moves with a velocity of 60 km/h 45 degree south of west Here the word velocity replaces both the words speed and direction
3.
(i) Uniform velocity: If a body covers equal distances in equal intervals of time, however small these intervals may be in a given direction, its velocity is said to be 'uniform velocity' So in uniform velocity a body moves with uniform speed in a given direction, for example, light travels with a uniform velocity of 3-10 m/s through the vacuum.
(ii) Variable velocity When a body travels unequal distances intervals of time or its direction changes or both change its velocity is said to be 'variable velocity' for example a bus turning at a junction has variable velocity.
4.
Point object Whenever the size of the object is much smaller than the distance it moves in a given time interval the size of the object can be neglected Then the object may be regarded as the point object.
Examples:
(i) A car covering a distance of 10 km can be treated as a point object.
(ii) Earth can be regarded as a point object for studying its motion around the sun
5.
Rest .A body is said to be at rest if it does not change its position with respect to its surroundings.A table lying in a room is at rest with respect to the walls of the room.
Motion .A body is said to be in motion if it changes its position with respect to its surroundings Thus , motion means movement of bodies A car running on the road is in motion with respect to the lamp posts,trees or bus stop on the roadside.
6.
Time taken = 2 min 20 s = 2 x 60 + 20 = 140 s
Radius,r = 100 m
In 140 s, the athlete will complete three and a half round
Distance covered = \(2\pi \) x 3.5
= 2 x \(\frac { 22 }{ 7 } \) x 100 x 3.5 = 2200 m.
At the end of his motion, the athlete will be in the diametrically opposite position
\(\therefore \) Displacement = diameter = 200 m
7.
Acceleration. In non-uniform motion, the velocity of a body changes with time It has different velocities at different instants of time and at different points of its path In such a situation we define a physical quantity called acceleration which is a measure of the change in the velocity of a body per unit time.
Acceleration is defined as the rate of change of velocity.If the velocity of a body changes from u to v in time t, then
Acceleration=\(\frac { Change\quad in\quad velocity }{ Time\quad taken } =\frac { Final\quad velocity-Initial\quad velocity }{ Time\quad taken } \)
or \(a=\frac { v-u }{ t } \)
As acceleration has both magnitude and direction, it is a vector quantity.
8.
Average speed. When the speed of the body varies with time we need to define its average speed.
Average speed is the total distance travelled by a body, divided by the total time taken to cover that distance Thus,
Average speed=\(\frac { Total\quad distance\quad travelled }{ Total\quad time\quad taken } \)
For example, if a car travels a distance of 10 km in 2 hours, then its
Average speed=\(\frac { 100\quad km }{ 2\quad hour } \) = 50 km per hour.
9.
| Distance | Displacement |
| 1.Distance is the length of the actual path traversed by a body irrespective of its direction of motion | 1. Displacement is the shortest distance between the initial and final position of a body in a given direction. |
| 2.Distance between two given points may be same or different for different paths chosen. | 2.Displacement between two given points is always same |
| It is a scalar quantity | It is a vector quantity |
| Distance covered is always positive or zero | Displacement covered may be positive negative or zero. |
10.
Non-uniform motion .If an object covers unequal distances in equal intervals of time,it is said to be in non-uniform motion. Most of the motions seen in our daily life are non-uniform. For example,if we drop a ball from the roof of a building we will note that the ball covers 4.9 m in the 1st second 14.7 m in the 2nd second 24.5 m in the 3rd second , and so on That is the ball covers increasingly larger distances in successive seconds as it falls down. Thus, the motion of a freely falling body is non-uniform
Other examples of non-uniform motion:
(i) A stone dropped from the top of a building
(ii) A ball thrown vertically upwards
(iii) The motion of a train as it leaves the station
(iv) The motion of a bus as it approaches a bus-stop
(v) The motion of a ball rolling down an inclined plane.
11.
( )
Speed of body is equal to total distance travelled by the body by the total time taken to travel that distance... its SI unit is kilometres per hour or miles per hour or metre per second.
12.
The odometer of an automobile measures the distance covered by an automobile.
13.
\(v_{ av }=\frac { s_{ 1 }+s_{ 2 } }{ t_{ 1 }+t_{ 2 } } =\frac { s }{ \frac { s_{ 1 } }{ v_{ 2 } } +\frac { s_{ 2 } }{ v_{ 2 } } } \)
\(40=\frac { 100 }{ \frac { 30 }{ 30 } +\frac { 70 }{ v_{ 2 } } } \)
\(=1+\frac { 70 }{ v_{ 2 } } =\frac { 100 }{ 40 } =\frac { 5 }{ 2 } \)
\(\frac { 7 }{ v_{ 2 } } =\frac { 5 }{ 2 } -1=\frac { 3 }{ 2 } \)
\(v_{ 2 }=\frac { 7X2 }{ 3 } =\frac { 14 }{ 3 } =4.67\quad km\quad h^{ -1 }\)
14.
(a)
20\(m/s^{ 1 }\)
15.
(b)
square of the time of fall
16.
(c)
acceleration
17.
(a)
30 \(ms^{ -2 }\)
18.
(c)
v = u + at
19.
(a)
\(ms^{ -1 }\)
20.
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