Sample Problem and Solutions in One Dimensional Motion

Linked Type Comprehensions
Four position -time graph are shown below.
a.

b.

c.

d.


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.
b.
c.
d.

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



a.
b.
c.
d.

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