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Sample Problem and Solutions in One Dimensional Motion



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Linked Type Comprehensions
Four position -time graph are shown below.
a.Sample Problem and Solutions in One Dimensional Motion

b.Sample Problem and Solutions in One Dimensional Motion

c.Sample Problem and Solutions in One Dimensional Motion

d.Sample Problem and Solutions in One Dimensional Motion


Question 5 What all graph shows motion with positive velocities
a. a and c only
b. all the four
c. b and D only
d. b only

Solution(5):
. The instantaneous velocity is given by the slope of the displacement time graph.
Since slope is positive in graph a and c.Positive velocity is there in a and c curve
Hence (a) and (c) are correct
Question 6. What all graph shows motion with negative velocities
a. a and b only
b. all the four
c. a and c only
d. c only

Solution(6):
. The instantaneous velocity is given by the slope of the displacement time graph.
Since slope is negative in graph b and d.Negative velocity is there in b and d curve
Hence (b) and (d) are correct
Question 7.which of the following graph correctly represents velocity-time relationships for a particle released from rest to fall under gravity
a.Sample Problem and Solutions in One Dimensional Motion
b.Sample Problem and Solutions in One Dimensional Motion
c.Sample Problem and Solutions in One Dimensional Motion
d.Sample Problem and Solutions in One Dimensional Motion

Solution(7):
.
The velocity will increase with time so b is the correct answer
Hence (b) is correct
Question 8.The v-x graph of a particle moving along a straight line is shown below.Which of the below graph shows a-x graph
Sample Problem and Solutions in One Dimensional Motion


a.Sample Problem and Solutions in One Dimensional Motion
b.Sample Problem and Solutions in One Dimensional Motion
c.Sample Problem and Solutions in One Dimensional Motion
d.Sample Problem and Solutions in One Dimensional Motion

Solution(8):
. The equation for the given graph is
v=-(v0/x0)x + v0 ---(1)
Differentiating both sides we get
dv/dx=-v0/x0 ---(2)
Now
a=v(dv/dx)
or
a=(-v0/x0)[-(v0/x0)x + v0 ]
or
a=mx+c
where m=v02/x0)2
and c=-v02/x0)2

So that means slope is positive and intercept is negative
So (d) is correct

More Practice Problems>
Question 1
A stone is thrown vertically upwards with a initial speed of 10 m/s from the edge of the roof of the house of Height H=20 m
a) how long does it takes for the stone to hit the ground
b) At what velocity it will hit the ground
Solution
t=3.28 sec
v=-22.2 m/s
Question 2
A body fell from rest from a height H above the ground. In the last 1 sec of the its fall, it travelled a distance H/2 . Find the value of H
Solution
H=57.1 m
Question 3
If the body loses half of its velocity on penetrating 3 cm in the wooden block,then how much will it penetrate more before coming to rest?
Solution
1 cm

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