Can you help unravel this hw problem?

Question

A time-varying net force acting on a 6 kg particle causes the object to have a displacement given by:
x = a + b t + d t^2 + e t^3
where a = 2.1 m
where b = 1 m/s
where d = - 2.3 m/s^2
and e = 0.97 m/s^3
with x in meters and t in seconds

Find the work done on the particle in the first 2 s of motion. answer in J

Still working on this one....any more ideas????

Answer 1

I don't think I've understood it clearly, but let's see.

First, you have to find the displacement of the particle:
x = 2.1 + 1*2 - 2.3*(2^2) + 0.97*(2^3) = 2.1+2-9.2+7.76 = 21.06m

Given the displacement, you'll need the force. To find the force, you need to find the acceleration. So, the second derivative of the displacement, which turns out to be:

a(2s) = 2*d + 6*e*t = 2*(-2.1) + 6*(0.97)*(2) = -4.2 + 11.64 = 7.44

So, the force in the first 2s is F = M*a(2s) = 6kg*7.44(m/s^2) = 44.64 N

The work is given by:

W = F*x(2s) = 44.64*21.06 = 940.1184 J

Hope I've helped on something.

Answer 2

Find the kinetic energy when t=0 and when t=2 and subtract.