Respuesta :
Answer:
31.232 kJ
Explanation:
Given,
mass of the particle, m = 4 Kg
Position of object as the function of time
[tex]x = 3.0 t - 4.0 t^2 + 1.0 t^3[/tex]
Work done by the object by the force from t = 0 to t = 8.0 s =?
we know,
[tex]v = \dfrac{dx}{dt}[/tex]
[tex]v =3-8t +3 t^2[/tex]
velocity at t = 0 s
u = 3 - 8 x 0 + 3 x 0 = 3 m/s
velocity at t= 8 s
v = 3 - 8 x 8 + 3 x 8 x 8
v = 125 m/s
Work done is equal to change in KE
[tex]W = \dfrac{1}{2}mv^2 - \dfrac{1}{2}mu^2[/tex]
[tex]W = \dfrac{1}{2}m(v^2 -u^2)[/tex]
[tex]W = \dfrac{1}{2}\times 4\times (125^2 -3^2)[/tex]
W = 31.232 k J
Hence, work done is equal to 31.232 kJ
Answer:
34304 Joule
Explanation:
mass of particle, m = 4 kg
x = 3t - 4t² + t³
Let v is the velocity
v = dx/dt = 3 - 8t + 3t²
Let a is the acceleration
a = dv/dt = - 8 + 6t
Work is defined as the product of force.
[tex]\int dW=\int madx[/tex]
[tex]W=4\times \int _{0}^{8} \left ( -24t+82 t - 72t^{2}+18t^{3} \right )dx[/tex]
[tex]W=4\times \left ( -24t+41t^{2} - 24t^{3}+4.5t^{4}\right )_{0}^{8}[/tex]
[tex]W=4\times \left ( -24\times 8+41\times 64 - 24\times 512+4.5\times 4096\right )[/tex]
W = 4 x (- 192 + 2624 - 12288 + 18432)
W = 34304 Joule
