Kinematics (Assignment)x - Vishwa Bharati Public School

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Nov 14, 2013 (3 years and 8 months ago)

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VISHWA BHARATI PUBLIC SCHOOL, NOIDA

ASSIGNMENT FOR CLASS
-
XI

Kinematics

Q.1


A car’s odometer reads 22687km at the start of a trip and 22791km at the end. The trip
took 4h. what

was the car’s average speed in km/h and m/s?


[Ans. 26km/h,
7.2m/s]


Q.2


The displacement time graph for two bodies A and B are straight lines inclined at 60
0

and
30
0

to the time axis. Find the ratio of their speeds.


[An
s. 3]


Q.3


Two cars A and B travel along the same direction from the same starting place. Car A
maintains a speed of 60km/h and car B 75km/h, but B starts one hour later. How many
hours will B take to overtake A?



[Ans. 300km]


Q.4


If two bodies move towards each other the distance between them decreases at a rate of
9m/s. When they move in the same direction with the same speeds, the distance between
them increases at a rate of 4m/s. find thei
r speeds.


[Ans. 6.5m/s, 2.5m/s]


Q.5


A car covers first half of the certain distance with speed v
1

and second half with speed v
2
.
Find the average speed of the whole journey.


[Ans. V
av

=
]


Q.6


A car
travels first half time with velocity v
1

and second half time with velocity v
2
. Find
the average speed of the whole journey.


[Ans.


Q.7


An automobile travels on a straight road for 40km at 30km/h. It then continu
es in the
same direction for another 40km at 60km/h. [a] What is the average velocity for the car
during this 80km trip? [b] What is the average speed? [c] graph x vs t and indicate how
average velocity can be found from the graph.



[Ans.
40km/h, 40km/h]


Q.8


If a particle position is given by x = 4


12t + 3t
2

where t is in seconds and x is in meters,
what is the velocity at t=1s? [b] Is it moving in positive or negative direction of ‘x’ just
then? [c] What

is the speed at that instant? [d] Is the speed larger or lesser at later times?
[try answering the next two questions without calculation] [e]Is there ever an instant
when the velocity is zero? [f] Is there time after 3 seconds when the particle is moving

in
the negative direction of ‘x’?

[Ans.
-
6m/s, negative direction, 6m.s, first smaller then zero and then larger , yes, no]

2
1
2
1
2
v
v
v
v

]
2
2
1
v
v


Q.9


A proton moves along the x axis according to equation x = 50t + 10t
2
, where x is in meter
and t in seconds. Calculate the
[a] average velocity of the proton during first 3 seconds of
its motion [b] the instantaneous velocity of the equation at t = 3 seconds [c] the
instantaneous acceleration of the proton at t = 3seconds. [d] Graph x vs t and indicate
how the answer to [a] ca
n be obtained from the plot [e] indicate the answer to B on the
graph [f] Plot v vs t and indicate on it the answer to [c]

[Ans. 80m/s, 110m/s, 20m/s
2
]


Q.10


What do quantities [dx/dt]
2
and d
2
x/dt
2

represent. What are their SI units?



Assignment No:2

[ Motion with constant acceleration]

Q.1


An antelope moving with constant acceleration covers the distance between two points
70m apart in 7 seconds. Its speed


as is passes the second point is 15m/s [a] what is the
speed at the first point? [b] what
is the acceleration?


[Ans. 5m/s, 1.43m/s
2
]


Q.2


The human body can survive a negative acceleration trauma accident if the magnitude of
acceleration is less than 250m/s
2
. if you are in auto mobile accident with initial speed of
105km/h and

are stopped by an airbag that inflates from the dashboard, over what
distance must the airbag stop you for you to survive the crash?


[Ans. 1.70m]


Q.3


An airplane travels 280m down the runway before taking off. If it starts from rest, mov
es
with constant acceleration, and becomes airborne in 8seconds, what is the speed in m/s
when it takes off?




[Ans. 70m/s]


Q.4


At the instant traffic light turns green, a car that has
been waiting at the intersection starts
ahead with a constant acceleration of 3.2m/s
2
. at the same instant a truck traveling with
constant speed of 20m/s , overtakes and passes the car. [a] How far beyond the starting
point does the car overtake the truck?

[b] how fast was the car traveling when it overtakes
the truck? [c] Sketch an x
-
t graph for motion of both the bodies. Take x=0 as the
intersection. [d] Sketch v
-
t graph for both the vehicles?




[Ans.12.5s, 250m]


Q.5


A brick is dropped fr
om the roof of the building. The brick strikes the ground in 2.5
seconds. You may ignore air resistance. [a] How tall is the building? [b] what was brick’s
velocity just before it hits the ground? [c] Sketch a
-
t, v
-
t and x
-
t graph for the motion.

[Ans. 30.
6m, 24.5m/s]


Q.6


A student throws a ball vertically downwards with 6m/s. [a] What is the speed after
falling for 2 seconds? [b] How far does in travel in 2 seconds? [c] What is the magnitude
of velocity after falling 10m?



[Ans. 25.6m/s, 31.6m,
15.2m/s]


Q.7


A subway train starts from at station and accelerates at a rate of 1.6m/s
2

for 14 seconds. It
runs at the constant speed for 70 seconds and slows down at a rate of 3.5m/s
2

until it
stops at the ne
xt station. Find the total distance covered.


[Ans. 1800m]


Q.8


A stone is dropped from the top of a cliff and is found to travel to travel 44.1m in the last
second before it reaches the ground. Find the height of the cliff.



[Ans. 122.5m]


Q.9


A body starting from rest, was observed to cover 20m in 1 second and 40m during the
next second. How far had it traveled before the first observation was taken?


[Ans.
2.5m]


Q.10


From the top of tower 100m high a ba
ll is dropped vertically and at the same instant
another ball is projected vertically upwards from the ground so that it just reaches the top
of the tower. At what height do the two balls pass one another.


[Ans. 75m from
ground]


Q.11


On turni
ng a corner ,a motorist rushing at 44m.s finds a child on the road 100m ahead. He
instantly stops the engine and applies brakes so as to stop within 1m from the child.
Calculate the time required to stop it.


[Ans. 4.5s]