# calculations

```Calculations
Practice
Acceleration

vf - vi
a t
Acceleration
the rate of change of velocity
 change in speed or direction

a
v f  vi
t
a:
vf:
v i:
t:
acceleration
final velocity
initial velocity
time
Calculations

You are traveling in a car that is moving at a velocity of 20 m/s.
Suddenly, a car 10 meters in front of you slams on it’s brakes. At
that moment, you also slam on your breaks and slow to 5 m/s.
Calculate the acceleration if it took 2 seconds to slow your car
down.
GIVEN:
vi = 20 m/s
t=2s
vf = 5 m/s
vf - vi
a=?
a t
WORK:
a = (vf - vi) &divide; t
a = (5m/s - 20m/s) &divide; (2s)
a = -15 m/s &divide; 2 s
a = -7.5 m/s2
Newton’s Second Law
F
a
m
F = ma
F
a
m
F: force (N)
m: mass (kg)
a: accel (m/s2)
1 N = 1 kg &middot;m/s2
Calculations
 A dock worker needs to stop a box of goods that is rolling across
a manual conveyer belt. The box has a mass of 8.35kg and is
accelerating at .75m/s2. How much force will he need to apply to
the box in order to stop it??
GIVEN:
F=?
m = 8.35 kg
a = .75 m/s2
F
m a
WORK:
F = ma
F = (8.35 kg)(.75 m/s2)
F = 6.26 N
Gravity

Weight

the force of gravity on an object
W = mg
MASS
always the same
(kg)
W: weight (N)
m: mass (kg)
g: acceleration
due to gravity
(m/s2)
WEIGHT
depends on gravity
(N)
Calculations

Ms. Stayner’s morbidly obese aunt Flossie
weighs 2695 N. What is her mass?
GIVEN:
F(W) = 2695 N
m=?
a(g) = 9.8 m/s2
F
m a
WORK:
m=F&divide;a
m = (2695 N)&divide;(9.8 m/s2)
m = 275 kg
Momentum

Momentum
 quantity of motion
• Use the unit
kg&middot;m/s
p
m v
p:
m:
v:
p = mv
momentum (kg&middot;m/s)
mass (kg)
velocity (m/s)
Momentum

A cannon fires a 40.5kg shell toward a target
and the shell moves with a velocity of
120m/s. Calculate the shell's momentum.
GIVEN:
p=?
m = 40.5 kg
v = 120 m/s
p
m v
WORK:
p = mv
p = (40.5 kg)(120 m/s)
p = 4860 kg&middot;m/s
```