Question

position of an object is related to tine as x=t^3-12t where x is in metre and t in second. find the acceleration of the object when its velocity is zero​

Answer 1

Step-by-step explanation:

$\frac{dx}{dt} = v$

$\frac{d( {t}^{3} - 12t) }{dt}$

${3t}^{2} - 12 = 0$

Here we equate it to 0, as the velocity is 0.

3t²=12

t²=4

t=2 sec (as time can't be negative)

Hence position of particle when velocity is 0 will be,

x=20+ t³-12t

x=20+ 2³-12(2)

x=20+8-24

x=4

As far as acceleration is concerned, if the initial and final velocities are 0,

acceleration automatically becomes 0.

Because,

a=dv/dt

change in velocity by time

substituting 0 in dv, we get a=0