At t = 15.0 seconds an object with mass 6 kg was observed to have a velocity of ‹ 9, 25, −9 › m/s. at t = 15.1 seconds its velocity was ‹ 18, 17, 21 › m/s. what was the average (vector) net force acting on the object?

Explanation:

Mass = 6 kg

Initial velocity = ‹ 9, 25, −9 › m/s

Initial time = 15.0 s

Final velocity = ‹ 18, 17, 21 › m/s

Final time = 15.1

Change in velocity = ‹ 18, 17, 21 › - ‹ 9, 25, −9 › = ‹ 9, -8, 30 › m/s

Change in time = 15.1 - 15.0 = 0.1 s

Acceleration = Change in velocity ÷ Change in time

Acceleration =  ‹ 9, -8, 30 › ÷ 0.1

Acceleration =  ‹ 90, -80, 300 › m/s²

Force = Mass x acceleration

Force = 6 x ‹ 90, -80, 300 › = ‹ 540, -480, 1800 › N

Average  net force acting on the object is ‹ 540, -480, 1800 › N

6.5 m

Explanation:

First of all, we need to compute the acceleration of the skier. We know that there is only force acting on the skier: the force of friction, which is in the opposite direction to the motion of the skier. Using 2nd Newton Law:

where is the force of friction, with

is the coefficient of kinetic friction

m is the mass of the skier

is the acceleration due to gravity

Re-arranging the equation, we find:

So now we can use the following SUVAT equation to calcualte the total displacement of the skier before stopping:

where

v = 0 is the final velocity

u = 5.30 m/s is the initial velocity

a = -2.16 m/s^2 is the acceleration

d = ? is the displacement

Solving the formula for d, we find: