5. The displacement (in metre) 1 point
of a particle moving along x -
axis given by x=5t + 4t2.
Calculate the instantaneous
velocity at t = 2s.
Answers
Given :
Displacement of particle is given by
To Find :
Instantaneous Velocity at t = 2sec
Theory :
• Velocity
The rate of change of displacement of a particle with time is called velocity of the particle.
• Instantaneous Velocity
The velocity of an object at a particular instant of time is called Instantaneous Velocity
Solution :
Displacement of particle given by
We have to find the Instantenuous velocity of the particle at t =2 sec
Now differnatiate with respect to t
We know that
Then ,
If t = 2 sec
Then,
Hence ,The Instantenuous Velocity of a particle At t =2 sec is 21m/s
_______________
More information about topic
- Velocity is a vector quantity.
- The velocity of an object can be positive, zero and negative.
- SI unit of Velocity is m/s
- Dimension of Velocity:
Answer:
Given :
Displacement of particle is given by
\sf\:x(t)=4t^2+5tx(t)=4t
2
+5t
To Find :
Instantaneous Velocity at t = 2sec
Theory :
• Velocity
The rate of change of displacement of a particle with time is called velocity of the particle.
\rm\:Velocity=\dfrac{Distance}{Time\:interval}Velocity=
Timeinterval
Distance
• Instantaneous Velocity
The velocity of an object at a particular instant of time is called Instantaneous Velocity
\sf\:V=\lim_{\triangle\:t\:\to0}=\dfrac{d\vec{x}}{dt}V=lim
△t→0
=
dt
d
x
Solution :
Displacement of particle given by
\sf\:x(t)=4t^2+5tx(t)=4t
2
+5t
We have to find the Instantenuous velocity of the particle at t =2 sec
\sf\:x=4t^2+5tx=4t
2
+5t
Now differnatiate with respect to t
\sf\dfrac{dx}{dt}=\dfrac{d(4t^2)}{dt}+\dfrac{d(5t)}{dt}
dt
dx
=
dt
d(4t
2
)
+
dt
d(5t)
We know that
\sf\dfrac{d(x^n)}{dx}=nx^{n-1}
dx
d(x
n
)
=nx
n−1
Then ,
\sf\:v=8t+5v=8t+5
If t = 2 sec
Then,
\sf\:v=8\times2+5v=8×2+5
\sf\:v=16+5v=16+5
\sf\:v=21ms^{-1}v=21ms
−1
Hence ,The Instantenuous Velocity of a particle At t =2 sec is 21m/s
_______________
More information about topic
Velocity is a vector quantity.
The velocity of an object can be positive, zero and negative.
SI unit of Velocity is m/s
Dimension of Velocity: \sf\:[M^0LT{}^{-1}][M
0
LT
−1
]