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Q 1. Write one main
difference between speed and velocity.
Solution
Q 2. A body leaving a
certain point "O" moves with a constant acceleration. At the end of
the 5th second its velocity is 1.5 m/s. At the end of the sixth second the
body stops and then begins to move backwards. Find the distance traversed by
the body before it stops. Determine the velocity with which the body returns to
point "O "?
Solution
The velocity slows 1.5
m/s in the sixth second so if the initial velocity direction is positive, the
acceleration isa = (dv/dt) = -1.5 m/s². Using the equation, v = u + at and
knowing that the return time to zero velocity will equal the approach time of 6
seconds. v = 0 + (- 1.5) × 6 v = -9 m/s So the velocity upon
returning to "O" is -9 m/s. The average velocity between
"O" and the stop point is v = (9 + 0) / 2 v = 4.5 m/s So the particle
travels d = 4.5 × 6 m → d = 27 m between "O" and the
stop points.
Q 3. A bus decreases its
speed from 80 km h-1 to 60 km h-1 in 5 s. Find
the acceleration of the bus.
Solution
Negative sign indicates
the bus is decelarating.
Q 4. A body travels from A
to B in 10 seconds with a speed of 50 km/h and returns with a speed of 100 km/h
in 5 s. Find the average speed. Also find the average velocity for the whole
journey.
Solution
Distance from A to B =
Speed x time
= 50 km/h x 10 s
=(50 km/h x 10 s) x
(5/18) ....
(to convert km/h to m/s
multiply by 5/18)
=1250 / 9
=139
m Total distance from A to B both ways = 139 m × 2
= 278 m Total time
taken = 10 + 5 = 15 s
Displacement is
zero, because the body has come back to its initial position.
Q 5. What is the quantity
which is measured by the area occupied below the velocity-time graph?
Solution
The distance is measured
by the area occupied below the velocity time graph.
Q 6. Give an example of
the motion of a body moving with a constant speed but with a variable velocity.
Draw a diagram to represent such a motion
Solution
The motion of a body in
a circular path with uniform speed has a variable velocity because in the circular
path, the direction of motion of the body continuously changes with time.
Q 7. A scooter starts from
rest and travels with a uniform acceleration of 2 ms-2 for 6
sec. What is the velocity acquired?
Solution
Initial velocity, u =0
(starts from rest) Final velocity, v = ? Time, t =6 s We know that
acceleration is a = (v - u)/t Therefore, velocity is v = u + at = 0 + 2
x 6 = 12 m/s
Q 8. A ball is
thrown vertically upwards. It rises up to a height of 20 m and comes back to
the initial position. Find: the total distance covered by the ball,
and the displacement of the ball.
Solution
The total distance
travelled = 20 m + 20 m = 40 m. Since, the ball returns to its initial
position, the initial and final positions coincide with each other. Hence, the
displacement of the ball = 0
Q 9. Explain average
speed.
Solution
The ratio of the total
distance travelled by the body to the total time of journey is called its
average speed. It is also the average of
values of speeds evaluated over equal intervals of time. Its SI unit is m/s.
Q 10. Define the
following terms: (a) speed (b) velocity (c) uniform velocity (d) non uniform
velocity
Solution
Speed Speed is the
distance travelled by a body in one second and is measured in metre per second
(m s-1) Velocity Velocity is the distance travelled by a body in a
particular direction in unit time Or Velocity is defined as the rate of change
of displacement. It is measured in metre per second (m s-1) Uniform
Velocity A body is said to travel with uniform velocity if it undergoes equal
displacement in equal intervals of time, however small in a given direction
Non-uniform Velocity A body is said to be moving with non-uniform or variable
velocity if it covers unequal distances in equal intervals of time or it covers
equal distances in unequal intervals of time or it covers equal distances in
equal intervals of time, but its direction is changing.
Q 11. What is the nature
of distance-time graphs for uniform and non-uniform motion of an object?
Solution
The distance-time graph
for uniform motion is a straight line (inclined at an angle to the time axis).
The distance-time graph for non-uniform motion can be a curve with increasing
or decreasing slope or any zigzag line.
Q 12. Distinguish between
average speed and average velocity.
Solution
Average speed is the
ratio of the total distance travelled by the body to the total time of journey,
it is never zero. If the velocity of a body moving in a particular direction
changes with time, then the ratio of displacement to the time taken in entire
journey is called its average velocity. Average velocity of a body can be zero
even if its average speed is not zero.
Q 13. Examine the data
given for the motion of two different objects A and B carefully and state
whether the motion of the objects is uniform or non uniform. Give reasons. Time
Distance travelled by object A in m Distance travelled by object B in m 9.30
a.m 10 12 9.45 a.m 20 19 10.00 a.m 30 23 10.15 a.m 40 35 10.30 a.m 50 37 10.45
a.m 60 41 11.00 a.m 70 44
Solution
Motion of object A is
uniform because it covers a distance of 10 km in every 15 minutes, that is
equal distances in equal intervals of time. Motion of object B is non-uniform
because it is covering unequal distances in equal intervals of time.
Q 14. Give the differences
between scalar and vector quantities.
Solution
Parameters
Scalar Quantities
Vector Quantities Definition The physical quantities
which have magnitude only are scalars. The physical quantities which have
magnitude and direction both are vectors. Example Mass, length, distance,
speed, etc. Displacement, velocity, acceleration, etc.
Q 15. What is the
acceleration in the case of uniform velocity ?
Solution
In the case of uniform
velocity, the speed or direction of a moving object is not changed and thus
there is no in acceleration. Therefore, in the case of uniform velocity the
acceleration will be zero.
Q 16. An object moves 18 m
in the first 3 seconds and 22 m in the next 3 seconds while it travels 14 m in
the last 3 seconds. Calculate the average speed.
Solution
Given data: s1 =
18 m, t1 =3 s, s2 = 22 m, t2 =3
s, s3 = 14 m, t3 = 3 s, average speed =?
Q 17. An object starting
from rest undergoes an acceleration of 10 m/s2. Find the distance
travelled in 5 seconds.
Solution
Given: u = 0, t = 5 s, a
= 10 m/s2 We know that
Q 18. Distinguish between
uniform velocity and variable velocity.
Solution
If a body travels equal
distances in equal intervals of time along a particular direction, then the
body is said to be moving with a uniform velocity. However, if a body travels
unequal distances in a particular direction in equal intervals of time or it
moves equal distances in equal intervals of time but its direction of motion
does not remain same, then the velocity of the body is said to be variable (or
non-uniform).
Q 19. A train starting
from a railway station and moving with uniform acceleration attains a speed of
40 km/h in 10 minutes. Find its acceleration.
Solution
Here we have, Initial
velocity, u = 0, Final velocity, v = 40km/h = 11.11m/s Time (t) = 10 minute =
60x10=600s Acceleration (a) =?
Q 20. What is retardation? Write its formula.
Given an example where it acts on a body.
Solution
Retardation is a
decrease in acceleration. This means that retardation is the rate of decrease
in velocity. A positive sign of the magnitude of acceleration shows increase in
velocity and a negative sign shows decrease in velocity. Formula: Example: When brakes
are applied to a moving bicycle, there is retardation in its
motion.
Q 21. What can you
say about the motion of an object if its speed-time graph is a straight line
parallel to the time axis?
Solution
When the slope of a
speed time graph is a straight line parallel to the time axis, the object is
moving with uniform speed.
Q 22. Speed is a scalar
quantity whereas velocity is a vector quantity. Thus, state one
difference between the two quantities important for distinguishing between
speed-time graphs and velocity-time graphs.
Solution
Speed cannot assume a
negative value whereas velocity can.
Q 23. An object moving in
a certain direction with acceleration in the perpendicular direction. Is this
situation possible? Give an example of such situation.
Solution
Yes, The above
given condition is possible. e.g. When a stone tied to a string is whirled in a
circular path, the acceleration acting on it is always at right angle to the
direction of motion of stone.
Q 24. A runner runs 1.0 km
south, then 2.0 km east, then 1.0 km north, and then 2.0 km west to return to
its starting point. This trip takes 50 minutes. What was the runner's average
speed, and what was the runner's average velocity?
Solution
Average
speed =Total distance / Total time Total distance = 1 + 2 + 1 + 2 = 6
km Time taken = 50minutes =50/60 hours=5/6 hours Average speed =
(6km) / 50 minutes = (6 km) / (5 / 6)hours = 7.2 km/hour
Displacement is zero, because the runner returns back to its starting point.
Total displacement = 0 Therefore average velocity = 0
Q 25. Is it possible that
displacement is zero but not the distance? Justify your answer.
Solution
Yes. If a
body is moving on a circular path,
then in one complete revolution the displacement
is zero but distance is equal to circumference of the circle.
Q 26. A motor boat
starting from rest on a lake accelerates in a straight line at a constant rate
of 6m/s2 for 6 s. How far does the boat travel during this
time?
Solution
Given, initial velocity
u = 0. Acceleration a = 6 m/s2 Time taken t = 6 s. Using the
second equation of motion, we get S = ut + ½ at2 S = 0 +
½ x 6 x 62 = 108 m
Q 27. Can the
distance-time graph of a moving body be a straight line perpendicular to time
axis? If not, why?
Solution
The distance-time graph
of a moving body as straight line perpendicular to time axis is not possible as
it represents different values of distance travelled at a particular time which
is not possible.
Q 28. Is the distance
covered by a body always greater than the magnitude of the displacement?
Solution
If the body is not
moving in a straight line, then the distance is always greater than the
magnitude of the displacement. If the body is moving in a straioght line, then
the distance is equal to the magnitude of displacement.
Q 29. In a velocity-time
graph, what does the area enclosed by the velocity-time curve and the time axis
represents?
Solution
The area enclosed by the
velocity-time curve and the time axis represents the distance travelled by the
body.
Q 30. What can you say
about the motion of an object whose distance-time graph is a straight line
parallel to the time axis?
Solution
When the slope of
distance-time graph is a straight line parallel to time axis, the object is at
the same position as the time passes. That means the object is at rest.
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