PHysics question

Question

A 4.60 kg particle moves along the x axis. Its position varies with time according to x = t + 1.8t3, where x is in meters and t is in seconds

(a) Find the kinetic energy at any time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.
K= ______J



(b) Find the acceleration of the particle and the force acting on it at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)
a=_____________m/s2
F=_____________N



(c) Find the power being delivered to the particle at time t. (Accurately round any coefficient to exactly two decimal places. Use t as necessary.)

P=__________W

Answer 1

KE = 1/2 mv²

 

Where v = dX/dt = (1+1.8x3xt²)

 

KE = 1/2 (4.6) (1+5.4t²)² J

Acceleration = dv/dt = d/dt ( 1+5.4 t² ) 

 

= 10.8t m/s² =a

Force = Massx acceleration = 4.6 x ( 10.8 t)

W = F X 

Power = Rate of doing work = dW/dt = d/dt (FX)

F (dX/dt) + X dF/dt = Force x Velocity + X M( da/dt)

= m*a* v + X*m* (10.8)

=4.6*10.8t*(1+5.4t²) +(t + 1.8t³)*4.6* 10.8 Watt