Question

The velocity of a particle moving on the x-axis is given by v = 2x2 + x where v is in m/s and x is in meter. Find its acceleration in m/s2 when passing the point x = 2m:

Answer 1

answer : 90m/s²

explanation : The velocity of a particle moving along x-axis is given by, v = 2x² + x

we have to find acceleration at x = 2m.

using application, a = v × dv/dx

so, first of all, differentiate v with respect to x.

i.e., dv/dx = d(2x² + x)/dx = 4x + 1

and then acceleration, a = v × dv/dx

= (2x² + 2)(4x + 1)

at x = 2,

Acceleration , a = (2 × 2² + 2)(4 × 2 + 1)

= (2 × 4 + 2)(8 + 1)

= 90 m/s²

hence, acceleration of the particle at x = 2m , is 90m/s²