Question

For a particle moving along x-axis, acceleration is given as a 2v particle is v0 at x = 0, find speed as a function of x.

Answer 1

please see attached file......

Answer 2

✌️✌️ hey mate,

a = 2v2

so, as a = dv/dt

dv/dt = 2v2.

dv/dx * dx/dt = 2v2 (multiply and divide by dx)

v dv/dx = 2v2.

dv/dx = 2v

1/v dv = 2dx

integrating both sides,

∫1/v dv =∫2dx

so, ln v = 2x + C

when x= 0, v = v0

so, ln v0 = C

so, ln v = 2x + ln v0

so, ln (v/v0) = 2x

v / v0 = e2x

v = v0e2x.

thanks...
nice to help you ✌️✌️