Question

The velocity - position graph of a particle moving in a straight line along x-axis is given below. Acceleration of particle at x =2m is
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Answer 1

v=2x²

as a=dv/dx

a=d(2x²)/dx

=4x

at x= 2m

a=4*2

=8 m/s

Answer 2

Answer:

a= 64 m/s²  

Explanation:

Given that

v= 2 x²

As we know that rate of change of velocity with time is known as acceleration.

$a=\dfrac{dv}{dt}$

If velocity given as a function of x the acceleration given as

$a=v\dfrac{dv}{dx}$

v= 2 x²

$\dfrac{dv}{dx}=4x$

At x= 2 m

v= 2 x 2²= 8 m/s

$\dfrac{dv}{dx}=4x$

$\dfrac{dv}{dx}=8s^{-1}$

$a=v\dfrac{dv}{dx}$

$a=8\times 8$

a= 64 m/s²