Question

1 pc
3. The displacement of a
particle is given by x(t)= 4 t^2
+8t m. Its velocity at t = 5 s is
m/s.​

Answer 1

Answer: 48m/s IS THE ANSWER.

Explanation:

v=dx/dt

 =8t+8=8(5)+8

  =48m/s.

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Answer 2

Given :

Motion of particle is given by

$\sf\:x(t)=4t^2+8t$m

To Find :

Velocity at t = 5 sec

Theory :

• Velocity

The rate of change of displacement of a particle with time is called velocity of the particle.

${\purple{\boxed{\large{\bold{Velocity=\frac{Distance}{Time\:interval}}}}}}$

In differential form:

$\sf\:Velocity,V=\dfrac{dx}{dt}$

Solution :

Motion of particle given by

$\sf\:x(t)=4t^2+8t$

We have to find the velocity of the particle at t = 5 sec

$\sf\:x=4t^2+8t$

Now differnatiate with respect to t

$\sf\dfrac{dx}{dt}=\dfrac{d(4t^2)}{dt}+\dfrac{d(8t)}{dt}$

We know that

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

Then ,

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

If t = 5sec

Then,

$\sf\:v=8\times5+8$

$\sf\:v=40+8$

$\sf\:v=48ms^{-1}$

Hence ,The Velocity of a particle At t =5 sec is 48m/s

$\rule{200}2$

More information about topic

1. Velocity is a vector quantity.
2. The velocity of an object can be positive, zero and negative.
3. SI unit of Velocity is m/s
4. Dimension of Velocity: $\sf\:[M^0LT{}^{-1}]$