Question

A particle of unit mass moves so that displacement after t seconds is given by x = 3 cos(2t 4) find the acceleration and kinetic energy at the end of 2 seconds. Formula for kinetic energy is k.
e. = 1 2 mv 2

Answer 1

Explanation:

x=3cos(2t−4)-----(i) mass=1

Step 1:

Acceleration is given by d2xdt2

Step 2:

Differentiating (i) twice, we get

dxdt=3(−2ssin(2t−4))=−6sin(2t−4)----(i)

d2xdt2=−6×2cos(2t−4)=−12cos(2t−4)----(ii)

Step 3:

When t=2

Acceleration =−12cos0=−12

The velocity after 2 sec is got by substituting t=2 in (i)

Velocity v=−6sin0=0

Therefore the K.E=12