Question

Please make me understand the meaning of this question. I hv the ans. but ,i cant understand the meaning.


A Force acts on a 30gm particle in such a way that the position og the particle as a function of time is given by x=3t-4t^2+t^3,where x is in metre and t is in second.The work done during the first four second_______????


Plz make me understand the meaning of the question, i m very confused.

Answer 1

Hello,
This is a easy question with an answer
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m = 20 gm = 0.020 kgx = 3 t - 4 t² + t³   mv = dx/dt = 3 - 8 t + 3 t²   m/sa = dv/dt = -8 + 6 t   m/s²Force = m a = 0.120 t - 0.160  N
Work done = dW = F dx = F * (dx/dt) * dt        dW = (0.120 t - 0.160) * (3 - 8 t + 3 t²) dt               = 0.360 t³ -  1.440 t² + 1.640 t - 0.480
W = integral of dW from t = 0 to 4 sec:     = 0.090 t⁴ - 0.490 t³ + 0.82 t² - 0.480 t ] ,  t = 0 to 4s     = 2.88 J
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Answer 2

Here you have been given mass of the object that is 30gm
Now as it is subjected to force and application of force results in displacement it's function is given to you that is
$x = 3t - 4 {t}^{2} + {t}^{3}$
Now using this formula and by differentiating it twice you will find the formula for acceleration which will be used to find value of acceleration at t=4 which if multiplied to mass will give the value of FORCE

Now calculate the displacement by above given function for t=4(as work is asked for first 4 second)

Now multiply force and displacement that will give you work and that is asked.

Now multiply force