Question

The displacement of particle is given by x = `2/lambda (1 - e^(-lambdat))`, the acceleration of particle at 2s when λ = 2s^–1 will be (Take `l`n 0.018 = – 4)

Options

• 0.088 m/s²

• 0.072 m/s²

• 0.142 m/s²

• 0.048 m/s²

Answer 1

0.072 m/s² 

Explanation:

x = `2/lambda (1 - e^(-lambdat))`

`(dx)/(dt) = v = - 2/lambda xx (e^(-lambdat)) xx lambda = -2(e^(-lambdat))`

∴ Acceleration will be, 

a = `(dv)/(dt) = 2 xx (e^(-lambdat)) lambda = 2lambda e^(-lambdat)`

At t = 2s, λ = 2s^–1

a = 2 × 2 × e^–4

= 2 × 2 × 0.018  ......(given)

∴ a = 0.072 m/s²