Exam (elaborations)
Chapter 13 Oscillations Non Periodic Motion
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Chapter 13 Oscillations Non Periodic Motion
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Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ®Chapter 2
Motion in a Straight Line
The study of motion of objects along a straight line is also known as
rectilinear motion .
Average Velocity and Average Speed
Average Velocity
Average velocity is defined as the ratio of total displacement to the total time interval.
𝐓𝐨𝐭𝐚𝐥 𝐝𝐢𝐬𝐩𝐥𝐚𝐜𝐞𝐦𝐞𝐧𝐭
Average velocity=
𝐓𝐨𝐭𝐚𝐥 𝐭𝐢𝐦𝐞 𝐢𝐧𝐭𝐞𝐫𝐯𝐚𝐥
𝐱 𝟐 −𝐱 𝟏 ∆𝐱
𝐯̅ = =
𝐭 𝟐 −𝐭 𝟏 ∆𝐭
where x1 and x2 are the positions of the object at time t1 and t2
Average speed
Average speed is defined as the ratio of total path length (distance travelled) to the
total time interval.
𝐓𝐨𝐭𝐚𝐥 𝐩𝐚𝐭𝐡 𝐥𝐞𝐧𝐠𝐭𝐡
Average speed=
𝐓𝐨𝐭𝐚𝐥 𝐭𝐢𝐦𝐞 𝐢𝐧𝐭𝐞𝐫𝐯𝐚𝐥
Uniform motion
If an object moving along the straight line covers equal distances in equal intervals of
time, it is said to be in uniform motion along a straight line .
In uniform motion velocity of the object remains constant.
Instantaneous Velocity and Speed
Instantaneous velocity
The average velocity tells us how fast an object has been moving over a
given time interval but does not tell us how fast it moves at different
instants of time during that interval. For this, we define instantaneous
velocity or simply velocity v at an instant t.
The velocity at an instant is called instantaneous velocity and is defined as
the limit of the average velocity as the time interval Δt becomes
infinitesimally small
𝚫𝐱 𝐝𝐱
v = 𝐥𝐢𝐦 =
𝚫𝐭→𝟎 𝚫𝐭 𝐝𝐭
𝐝𝐱
v = 𝐝𝐭
dx
is the differential coefficient of x with respect to t .It is the rate of
dt
change of position with respect to time.
, Join Now: https://join.hsslive.in Downloaded from https://www.hsslive.in ®
Determining velocity from position-time graph. Velocity at t = 4 s is the
slope of the tangent to the graph at that instant.
We see from Table 2.1 that as we decrease the value of ∆t from 2.0 s to
0.010 s, the value of the average velocity approaches the limiting value
𝐝𝐱
3.84 m s–1 which is the value of velocity at t = 4.0 s, i.e. the value of
𝐝𝐭
at t = 4.0 s.
Instantaneous speed
Instantaneous speed or simply speed is the magnitude of velocity.
For example, a velocity of 24 m s –1 and a velocity of – 24 m s –1 — both
have an associated speed of 24.0 m s -1 .
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