PHYSICS I EQUATIONS

Unit Conversion

a. 55 km to m

55 km x (1000 m / 1 km) = 55, 000 m

b. 12g to kg

12 kg x (1 kg / 1000 g) = 0.012 kg

c. 85 m/s to kph

85 m/s x (1 km / 1000 m) x (3600 s / 1 hour) = 306 kph

Uncertainty and Error

Percent Error = (| x - x_r | / x_r) x 100

• x_r = true or accepted value

• x = measured value

Percent Difference = (|x₁ - x₂| / x₁ + x₂ / 2) × 100

Mean (μ) = (Σ_x) / N

• Σ_x = sum of all values

• N = number of values.

Variance (σ²) = Σ (x_i - μ)² / N

• σ² = variance

• x_i = each value

• μ = mean

• N = number of values

Standard Deviation (σ) = √(Σ(x_i - μ)² / N)

Absolute Uncertainty = ± (Maximum Value - Minimum Value) / 2

Ex. Resistance of a wire 25.00 Ohm ± 0.05 Ohm

Range of Resistance 24.95 - 25.05 Ohm

• 25.05 - 24.95 / 2

• = 0.05 Ohm

Relative Uncertainty = (Absolute Uncertainty / Measured Value) × 100%

Ex. 0.05 Ohm / 25.00 Ohm x 100 = 0.2%

Rule 1: If data are to be added, add their absolute uncertainties.

Ex. Perimeter = sum of all the sides = 2(L +W)

• = 2(6.5m ± 0.1m + 3.4m ± 0.2m)

• = 2(9.9m ± 0.3m)

• = 19.8m

Rule 2: If data are to be multiplied or divided, add their relative uncertainties.

Ex. The area of a rectangle = L x W

• Relative uncertainty for length = 1.54%

• Relative uncertainty for width = 5.88%

• Sum = 7.42%

• = ((7.42%)(22.1m²) / 100%) = 1.64m² - absolute uncertainty.

Vector Addition

Angle of Vector (θ) = tan^-1[Σ_y / Σ_x]

Kinematic Equation of Motion

Speed (s) = d / t

• d = Distance

• t = Time

Velocity (v) = s / t

• s = displacement

• t = time

Average Speed (s_avg) = d_t / t_T

• d_t = Total Distance

• t_T = Total Time

Average Velocity (v_avg) = Δx / Δt = x - x₀ / t - t₀

• Δx = change in position

• Δt = change in time.

Instantaneous Velocity (v_ins) = lim(Δt → 0) (Δx/Δt)

Acceleration (a) = v - u / t

• u = Initial Velocity

• v = Final Velocity

• t = Time

Instantaneous Acceleration (a_ins) = lim(Δt → 0) (Δv/Δt)

• Δv = change in velocity

• Δt = change in time

Free Fall

V_F = V_i + gt

d = V_i t+ (1/2)gt²

V_F² = V_i² + 2gd

• V_F = Final Velocity

• V_i = Initial Velocity

• g = acceleration due to gravity

• d = displacement

• t = time elapsed

Projectile Motion

Horizontal Distance (d_x) = V_xt

• V_x = Horizontal Velocity

• t = time

Vertical Distance (d_y) = (1/2)gt²

• g = acceleration due to gravity

• t = time

Horizontal Velocity (v_x) = constant

Vertical Velocity (v_y) = gt

• g = acceleration due to gravity

• t = time

Time (t) = √(2d_y / g)

• d_y = Vertical Distance

• g = acceleration due to gravity

Actual Velocity (v) = √((v_x)² + (v_y)²)

• v_x = Horizontal Velocity

• v_y = Vertical Velocity

Projectile Motion with an Angle

Initial Velocity X (v_xi) = v_i cos θ

• v_i = Initial Velocity

• θ = Angle

Initial Velocity Y (v_yi) = v_i sin θ

• v_i = Initial Velocity

• θ = Angle

Actual Final Velocity (v) = √((v_xf)² + (v_yf)²)

• v_xf = Final Horizontal Velocity

• v_yf = Final Vertical Velocity

Distance X (d_x) = v_xit

• v_xi = Initial Horizontal Velocity

• t = time

Maximum Height (h_max) = (2v_isin θ)² / 2g

• v_i = Initial Velocity

• θ = Angle

• g = gravity

Time (t) = 2(v_i sin θ) / g

• v_i = Initial Velocity

• θ = Angle

• g = gravity