Question

The velocity of the particle moving along X-axis is given as V=3X , acceleration of the particle at X=2m is​

Answer 1

Answer: 18m/s^2

Explanation:

Acceleration =v×(dv/dx)

a = v × (d(3x)/dx)

a = 3x × 3

a = 3×2×3 = 18 m/s^2

Answer 2

Answer:$a=18 m/s^2$

Explanation:

Given

Velocity of Particle is v=3x

$\frac{\mathrm{d} x}{\mathrm{d} t}=3x$

$\frac{dx}{x}=3dt$

$\int \frac{dx}{x}=3\int dt$

$x=e^{3t}$

thus acceleration is given

$a=\frac{\mathrm{d^2} x}{\mathrm{d} t^2}=9e^{3t}$

$a=9e^{3t}$

at x=2 m

$t=\frac{\ln 2}{3}=0.231 s$

therefore acceleration

$a=9e^{\ln 2}$

$a=18 m/s^2$