Force & Motion

Calculations Practice

Manipulating the Formulas

d

s t

x

F

m a

x

m

D V

x

W

F d

x

#1

• A balance and a graduated cylinder are used to determine the density of a mineral sample. The sample has a mass of 14.7 g and a volume of 2.2 cm3. What is the density of the mineral sample?

m

D V

x

14.7

D V

x

14.7

D 2.2

x

D = 6.68 g/cm3

#2

• A cross country runner is able to maintain a pace of 2.5 m/s for a total distance of 350 m. How long does it take the runner to complete her run?

d

s t

350

s t

350

2.5 t

t = 140 s (2.3 min)

#3

• How far does a horse run if it maintains a speed of 11.2 m/s for 180 s?

d

s t

d

11.2 t

d

11.2 180d = 2016 m

#4

• If the volleyball player strikes the volleyball with a force of 1 N and the acceleration of the ball after being hit is 4 m/s2, what is the mass of the volleyball?

1 N

F

m a

x

1

m a

x

1

m 4

x

m = 0.25 kg

#4

• A 50 kg rocket generates 1000 N of thrust. What will be its acceleration if it is launched straight up?

F

m a

x

1000

m a

x

1000

50 a

x

a = 20 m/s2

#6• How far will this box be moved

if the mover applies 4 N of force to receive 142 J of work?

W

F d

x

142

F d

x

142

4 d

x

d = 35.5 m

More Practice7. What is the acceleration of a 70 kg mass being

pulled by a 140 N force?8. The world’s fastest passenger elevator operates at

an average speed of about 10 m/s. If the 60th floor is 219 m above the first floor, how long does it take the elevator to go from the first floor to the 60th floor?

9. What force do you have to apply to a car with a mass of 1454 kg to do only 110 J of work moving the car 20 m?

a = 2 m/s2

t = 21.9 s

F = 5.5 N

More Practice10. You found a strange rock and find that it has a

mass of 50.6 g. When placed in a graduated cylinder, the volume rises from 25 mL to 36.5 mL. What is the density of your rock?

(HINT: First, find the volume of the rock)

V = 36.5 – 25 = 11.5 mL

D = 4.4 g/mL

11. An airplane traveled 300 km northeast in 2 hours. Find the velocity of the plane.

12.A hockey puck slides on the ice for 3 seconds before crossing the goal line 6 meters away. What was the average speed of the puck?

13.You decide to throw a pen with a mass of 20 grams with a force of 40 N. What is the acceleration of the pen?

V = 150 km/s NE

s = 2 m/s2

a = 2 m/s2

14. An object pushed with a force of 10 N travels 30 m in 60 s. What is the objects speed?

A 2 m/sB 0.5 m/sC 6 m/sD 3 m/sE Not there

15. A paper airplane is traveling towards a student. The airplane travels 6 m in 2 s before hitting the student. What is the velocity of the plane?

A 3 m/sB 0.3 m/sC 3 m/s toward the studentD 0.3 m/s toward the studentE Not there

16. If you wanted to make an object with a mass of 30 g accelerate at 5 m/s2, how much force would be required?

A 150 NB 6 NC 15 ND 180 NE Not there