physics 10 59N?

Question

A 0.23 kg puck is initially stationary on an ice surface with negligible friction. At time t = 0, a horizontal force begins to move the puck. The force is given by = (14.9 - 2.79t2) , with in newtons and t in seconds, and it acts until its magnitude is zero. (a) What is the magnitude of the impulse on the puck from the force between t = 0.534 s and t = 1.76 s? (b) What is the change in momentum of the puck between t = 0 and the instant at which F = 0?

Answer 1

Have you learned calculus?
(a) [integral](t: 0.534 to 1.76) (14.9 - 2.79t^2)dt
= (14.9t - 0.93t^3) [evaluate from 0.534 to 1.76)
= 14.9*(1.76-0.534)-0.93*(1.76^3-0.534^3)
= 13.3 (N*s)
(b) The time when F = 0 is:
T = sqrt(14.9/2.79) = 2.31(s)
[integral](t: 0.00 to 2.31) (14.9 - 2.79t^2)dt
= (14.9t - 0.93t^3) [evaluate from 0.00 to 2.31)
= 14.9*2.31-0.93*2.31^3
= 23.0 (N*s) = 23.0(kg*m/s)