A luge and its rider, with a total mass of 67 kg, emerge from a downhill track o

Question

A luge and its rider, with a total mass of 67 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 28 m/s. If a force slows them to a stop at a constant rate of 3.4 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force? What are (d) F, (e) d, and (f) W if they, instead, slow at 6.8 m/s2?

I would like to learn how to solve this problem so please show steps. Thank you.

Explanation / Answer

F = m*a

= 67*3.4

= 227.8 N

b) Let u is the initial speed, v is the final speed and d is the distance travelled before coming to rest.

Apply Kinematic equation,

v^2 - u^2 = 2*a*d

d = (v^2 - u^2)/(2*a)

= (0^2 - 28^2/(2*(-3.4))

= 115.3 m

c) Work done by the force = change in kinetic energy

= 0.5*m*v^2 - 0.5*m*u^2

= 0 - 0.5*67*28^2

= -26264 J

d)

F = m*a

= 67*6.8

= 455.6 N

e) d = (0^2 - 28^2)/(2*6.8)

= 57.65 m

f) Workdone, W = 0.5*m*v^2 - 0.5*m*u^2

= 0 - 0.5*67*28^2

= -26264 J

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