The space s described in time t by a particle moving in a straight line is given by s = t 5 – 40t 3 + 30t 2 + 80t – 250 Find the minimum value of acceleration.

Question

Philoid · Accepted Answer

Given:

The Distance(S) covered by a particle in time t is given by

⇒ S = t⁵ - 40t³ + 30t² + 80t - 250

We know that acceleration of a particle is given by .

⇒

We need acceleration to be minimum,

We know that for maxima and minima,

⇒

⇒ t² = 4

⇒ t = 2 (∵ Time cannot be negative)

Differentiating ‘a’ again,

⇒

At t = 2

⇒

⇒ >0(Minima)

We get minimum for t = 2 sec,

The corresponding acceleration at t = 2 sec is,

⇒ a = 20(2)³ - 240(2) + 60

⇒ a = 160 - 480 + 60

⇒ a = - 260

∴ The minimum acceleration is - 260.

The space s described in time t by a particle moving in a straight line is given by s = t5 – 40t3 + 30t2 + 80t – 250 Find the minimum value of acceleration.

The space s described in time t by a particle moving in a straight line is given by s = t⁵ – 40t³ + 30t² + 80t – 250 Find the minimum value of acceleration.