Question

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.​

Answer 1

Given :

Displacement of particle is given by

$\sf\:x(t)=4t^2+5t$

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.

$\rm\:Velocity=\dfrac{Distance}{Time\:interval}$

• Instantaneous Velocity

The velocity of an object at a particular instant of time is called Instantaneous Velocity

$\sf\:V=\lim_{\triangle\:t\:\to0}=\dfrac{d\vec{x}}{dt}$

Solution :

Displacement of particle given by

$\sf\:x(t)=4t^2+5t$

We have to find the Instantenuous velocity of the particle at t =2 sec

$\sf\:x=4t^2+5t$

Now differnatiate with respect to t

$\sf\dfrac{dx}{dt}=\dfrac{d(4t^2)}{dt}+\dfrac{d(5t)}{dt}$

We know that

$\sf\dfrac{d(x^n)}{dx}=nx^{n-1}$

Then ,

$\sf\:v=8t+5$

If t = 2 sec

Then,

$\sf\:v=8\times2+5$

$\sf\:v=16+5$

$\sf\:v=21ms^{-1}$

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: $\sf\:[M^0LT{}^{-1}]$

Answer 2

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

]