Formulas And Calculations

Question 0

How do you calculate speed?

Answer 0

Speed (v) = distance travelled (d) / time taken (t)

v = d / t

Question 1

How do you calculate acceleration?

Answer 1

Acceleration (a) = change in velocity / time taken (t)

Charge in velocity = final velocity (v) - initial velocity (u)

a = (v - u) / t

Question 2

How do you calculate the gradient/acceleration from the line on a velocity-time graph?

Answer 2

• make two points on each axis, as far up and down the line as possible
• y1, y2, x1, x2

Gradient = (y2 - y1) / (x2 - x1)

Question 3

How do you calculate the distance travelled from the area underneath a velocity-time graph?

Answer 3

1) calculate the area of the rectangle / square:

Base x Height

2) calculate the area of the triangle

1/2 x Base x Height

3) calculate the area of one graphical square
4) multiply the value of one graphical square by the total number of squares

Question 4

On a standard school ticker timer set up, what amount of time does each length of tape represent and how would you work out the velocity from the length of tape?

Answer 4

• each length of tape represents 0.1s

- v = d (length of tape) / t (0.1s)

Question 5

How do you calculate the resultant force?

Answer 5

Simply add the forces acting on an object together and the result is the resultant force.

For example, two forces, one 25N and one of 30N act on an object with a resultant force of 55N (25 + 30)

Question 6

How do you calculate force?

Answer 6

Force = mass x acceleration

F = ma

Question 7

How can you calculate acceleration by rearranging Newton’s famous equation?

Answer 7

Acceleration = force / mass

a = F / m

Question 8

How do you calculate weight?

Answer 8

Weight (W) = mass (m) x gravitational acceleration (g)

W = mg

Question 9

How do you calculate momentum?

Answer 9

Momentum (p) = mass (m) x velocity (v)

p = mv

Question 10

How do you calculate an increase in momentum?

Answer 10

Increase in momentum = mv - mu

Initial momentum of an object = mu
Final momentum of an object = mv

Question 11

Rearrange the following formula, and explain what needs to be constant in order to make the rearrangement possible:

F = (mv - mu) / t

Answer 11

F = (mv - mu) / t
F = m(v - u) / t
(v - u) / t = a

F = ma

This rearrangement is possible so long as the MASS of the object is constant

Question 12

Force x time = ?

Answer 12

Force x time = increase in momentum

Question 13

How do you calculate the moment of a force?

Answer 13

Moment (Nm) = force (N) x perpendicular distance from pivot (d)

Moment = F x d

Question 14

A child weighs 150N and sits 2m from the middle of a see-saw…

Moment = 150N x 2m = 300Nm

If an adult weighing 600N was to sit on the other side and balance the see-saw, they would have to sit 0.5m from the fulcrum…

Moment = 600N x 0.5m = 300Nm

How would you solve this in one step?

Answer 14

150 x 2 = 600 x d

150 x 2 / 600 = d

= 0.5m

Question 15

How do you calculate orbital speed?

Answer 15

Orbital speed = 2 x pi x orbital radius (r) / time period (T)

2 x pi x r / T

T = time taken for a complete orbit

Question 16

What is the formula for calculating current?

Answer 16

I = Q / t

Or…

I = P / V

I = current in amps
Q = charge in coulombs
T = time in seconds
P = power in watts
V = voltage in volts

Question 17

How do you calculate potential difference?

Answer 17

V = W / Q

Or

V = I x R

V = potential difference in volts
W = energy transferred in joules
Q = charge in coulombs
I = current in amps
R = resistance in Ohm's

Question 18

How do you calculate charge?

Answer 18

Q = I x t

Q = charge in coulombs
I = current in amps
t = time in seconds

Question 19

How do you calculate power?

Answer 19

P = I x V

P = power in watts
I = current in amps
V = voltage

Question 20

How do you calculate energy?

Answer 20

W = V x Q

Or

W = P x t

W = energy in joules
P = power in watts
t = time in seconds
V = potential difference 
Q = charge in coulombs

Question 21

What equation would you use to calculate the cost of running a household appliance?

Answer 21

Cost in pence = power in kW x time in hours x cost per kWhr

Question 22

How do you calculate the speed of a wave?

Answer 22

Wave speed is related to its frequency and wavelength as follows:

Wave speed (m/s) = frequency (hertz) x wavelength (metres)

Question 23

What is the formula for the speed of sound?

Answer 23

Speed of sound = frequency x wavelength

V = f x λ

Question 24

How would you find and calculate the frequency of a sound by using a cathode ray oscilloscope?

Answer 24

• find the time period (T) for one complete wave (this can be seen and calculated from the display of the CRO)
• f = 1 / T

Eg: a CRO shows the T for a sound is 0.005 s

f = 1 / T

f = 1 / 0.005 s

f = 200 Hz

Question 25

What is Snell’s law of refraction?

Answer 25

n = sin i / sin r

Where…

n = refractive index of the material
i = angle of incidence in degrees
r = angle of refraction in degrees

Question 26

How do you calculate the critical angle?

Answer 26

sin c = 1 / n

Where…

c = the critical angle in degrees
n = the refractive index

Question 27

If you put energy into an efficient device it will convert a greater proportion of it into the desired form of output energy. It will use less energy to do the use job and as such, cost less to run.

How do you calculate efficiency?

Answer 27

Efficiency = useful energy output / total energy output

Question 28

How do you calculate efficiency?

Answer 28

Efficiency = useful energy output / total energy output

Question 29

How do you convert from m/s to km/h?

Answer 29

Multiply by 3.6

Question 30

What is the formula for calculating force from pressure?

Answer 30

Force (F) = pressure (p) x area (a)

Question 31

What is the formula for gravitational potential energy?

Answer 31

GPE = m x g x h

GPE = gravitational potential energy in Joules
m = mass of object in kilograms
g = gravitational field strength in N/kg
h = height above the ground in metres

Question 32

What equation shows the relationship between kinetic energy (J), mass (kg) and speed (m/s)?

Answer 32

kinetic energy = 1⁄2 × mass × speed2