4. Formulas related to distance, displacement, velocity and ac | Arihant Books | DC Pandey Books ™
4. Formulas related to distance, displacement, velocity and accelration
d = vt
d = at²
d = (vf + vi/2) ×t
d = 5t² (for distance in 'n' seconds)
d = 5(2tn - 1) (for distance in 'nth' second)
d = 1/2 mv²/F
d = vit + 5t²
d = v × underroot 2H/g
d = vt = x°wt = x°2pi/T × t = x°2pift
x = x° Sin wt
x = x° Sin (underroot k/m) t
vf = vi + at
2as = vf² - vi²
2as = (vi + at)² - vi²
2as = vf² - (vf - at) ²
v = underroot Vfx² + Vfy²
v = Power/Force
v = 2×K.E/momentum (k.e = 1/2 Pv)
v² = 2×Power×time/mass (P = mv²/2t)
v = underroot 2as
v = underroot gr (speed at highest point in a verticle circle)
v = underroot 5gr (speed at lowest point in a verticle circle)
v² = 2FS/m
v² = 2E/m
v² = 2Ve/m
v = eBr/m (velocity of particle under action of magnetic force along circular path)
v² = Force/Area.Density
v = w underroot x°² - x²
v = underroot k/m × underroot x°² - x²
v = x°w (at mean position where x=0)
v = x° underoot k/m
v = v° underroot 1 - x²/x°² (for determining ratio b/w inst. Velocity and maxi. Velocity)
v= x°2pif = x°2pi/T
a = x°w² = x°w.w = vw = v.2pif
Common velocity = m1v1/m1+m2
vi² = Rg/Sin2theta
v = underoot Tension×length/mass
V = 2pi ke²/nh (speed of e- in nth orbit)
Vn = V/n
v = nh/2pimr (lambda = 2pir and lambda=h/p)
ma = kx
a = kx/m (SHM)
a = - gx/l (Simple pendulum)
ac = v²/r
5. Formulas related to wavelength 'w'
w = v/f
w = 1/wave number
w1 = 2l (when pipe is opened at both ends)
w1 = 4l (when pipe is opened at one end)
Delta w = Us/f (doppler shift)
Wavelength for obs. = w - delta w = v/f - Us/f
w = hc/Ve
w = hc/E
w = h/mv
w = h/P as P = underroot 2mE so
w = h/underroot 2mE (de Broglie wavelength)
w = underroot 150/V A° (short method for de Broglie wavelength. This formula is applicable only for e-)
1/w = RH (1/p²-1/n²)
Wmaxi/Wmini = n²/n²-p² (for determining ratio b/w maxi. Wavelength to mini. Wavelength for series of atomic spectrum)
w = 2pir/n (n is no. of loops in a circle)
h/mv = 2pir
