Question

A 4.00-kg particle moves along the x axis. Its position varies with time according to x = t + 2.0t^3, where x is in meters and t is in seconds. Find (a) the kinetic energy of the particle at any time t, (b) the acceleration of the particle and the force acting on it at time t, and (c) the work done on the particle in the interval t = 0 to t = 2.00 s.​

Answer 1

Answer:

(a) KE=1/2m(6t+1)²

(b) a=6

(c) W=432joule

(a) x=t+2t³

differentiating it to find velocitie

dx/dt=6t+1=velocity

Kinetic energy =1/2m(6t+1)²

(b) dv/dt=acceleration=6m/s²

(c) Work done=F.x

F=m.a=4*6=24

at t=2sec,

x=2+2*2³

=2+16=18

W=18*24=432 joule