Motion Exercises

Motion exercises

1.    A car moving at 36km/h is uniformly accelerated at the rate of 0.5m/s.

a.    What is the speed of the car 6s after the acceleration begins?

v_f=v_i+a*t→ v_f=10.83+.5*6=13.83m/s 

b.    How far does the car move during the 6s

d=(v_i+v_f)/2*t→d= (36+39)/2*6=225m 

2.    A ball rolls down a hill accelerating at 3m/s.

a.    How far did it move in 4s if it starts from rest?
     v_f=v_i+a*t→v_f= 0+3*4=12m/s
     d=(v_i+v_f)/2*t→d=(0+12)/2*4=24m

b.    What is its speed after the 4s?

v_f=v_i+a*t→v_f= 0+3*4=12m/s

3.    Pressing the brake of a car it slows down from 30m/s and comes to stop during 6s.

a.    What is its stopping distance?

d=(v_i+v_f)/2*t→d=(30+0)/2*6=90m

b.    What is its acceleration?

 v_f=v_i+a*t→0=30+a*6→ -30=6a→a=-5m/s^2

4.    Two cars are moving at 30m/s. One car starts accelerating at 0.2m/s.(the other car continues in the same speed). What will the distance between the two cars be 4s after the acceleration started?

Car 1: v_f=v_i+a*t→v_f=30+.2*4=30.8m/s^2

            d=(v_i+v_f)/2*t→d=(30+30.8)/2*4=121.6m

Car 2: d=(v_i+v_f)/2*t→d=(30+0)/2*4=60m

Distance between the two: 121.6-60 = 51.6m

5.    An object moving at 20m/s starts accelerating at -0.5m/s covering a distance of 20 m. How long does this motion take?

d= v_i*t+1/2*a*t^2→20=20*t+1/2*-0.5t^2→0=-0.25t^2+20t-20→t=1.01s