How would I find acceleration from distance and velocity?

Question

My question is: a 99 kg water skier floating in a lake is pulled from rest to a speed of 11 m/s in a distance of 25 m. What is the net force exerted on the skier, assuming his acceleration is constant?

 

I obviously need to find acceleration first, so I can do f=ma. I did d=v0t, with 25=11t, which led me to 25/11=t. However, when I plugged this into f=ma as f=99(4.4), I got 435.6, which doesn't make sense contextually. What am I doing incorrectly?

 

Thanks in advance,

Answer 1

Since you are given the travel distance and the initial and final speeds, use the appropriate kinematic relation to find acceleration, and then get force from the mass and acceleration.

 

v₂² - v₁² = 2ad ⇒

 

a = (v₂² - v₁²)/(2d)

 

v₁ = 0  [started from rest]

v₂ = 11 m/s

d = 25 m

 

a = (11² - 0²)/[2(25)] m/s² = 2.42 m/s²

 

F = ma = (99 kg)(2.42 m/s²) = 239.58 N