Just use Newton's Second Law.
Hi, I'm currently revising and I have a question relating to Particle Motion. The question grows, but to get started I have to show that
Words do not express how grateful for any help I would be! I'd like to understand how to do this. Thanks.The acceleration, a m/s^2, of the particle, is
a = sin t + 4
Given that m = 6 (kg) and F(t) = 6 sin t + 24N
Well, all you've shown is the value of the acceleration at t = 0. That doesn't finished the job, at least as stated in the OP. Incidentally, you really need to put parentheses in your expression. What you've actually written is
a = 6 sin t + (24[N] / 6),
when you really meant
a = (6 sin t + 24[N]) / 6.
To finish the problem, just divide the 6 out term-by-term. You're almost there!
So now take the integral to get the velocity and don't forget that v(0)=0(the particle started from rest.)
Now do the same thing to find the position! See if you can finish from here.
I just need to see it happen step by step. Thanks again.(b) Given that initially the particle starts from rest at a particular datum point on the line of motion, show that the distance travelled, x, from the datum point by the particle at time t is,
x = 2 t^2 + t -sin t
Hence, show that the time taken for the particle to travel 8 m from the datum point is given by the solution of the equation f(t)=0 where:
f(t) = 2 t^2 + t - 8 -sin t
Now use the initial condition
to solve for c.
Now just do the exact same thing except this time velocity is the derivative of position this gives
The answer you got above. See if you can finish from here.