Do you mean: u² + 2u + 1 - v²? If so then= (u + 1)2 - v2= [(u + 1) + v][(u + 1) - v]= (u + 1 + v)(u + 1 - v)
1/f = 1/u+1/v Subtract 1/v from both sides: 1/f-1/v = 1/u Multiply all terms by fv: fv/f - fv/v = fv/u => v-f = fv/u Multiply all terms by u: u(v-f) = fv Divide both sides by v-f which will then make u the subject of the formula: u = fv/v-f
If: v = u+at Then: -u = -v+at or u = v-at (by dividing all terms by -1) a = (v-u)/t t = (v-u)/a
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1 equation: as u know that a=(v-u)/t so, v-u=a*t therefore, v=u+at which is the first equation of motion
1/v+1/u = 1/f
The SUVAT equations: s=ut + 1/2at^2 v= u + at v^2 = u^2 + 2as s=1/2(u+v)t s = displacement u= initial velocity v= final velocity a= acceleration t= time
Given f = 15 cm. Magnification = 3. So the ie v/u = 3. So v = 3u Using lens formula, 1/f = 1/v - 1/u Now u = -u and v = -3u and f = 15 Plug these. 1/15 = -1/3u + 1/u Hence u = 10 cm. The object is to be placed at a distance of 10 cm from the lens.
At First lets make you clear about symbolsv=Final velocityu=Initial Velocityt=TimeS=Distancea=AccelerationS=vt-(1/2)at2Proof of the formulaDistance=Speed(AV) * Time As a=(v-u)/tS= {(u+v)/2}*t v=u+atS={(v-at+v)/2}*t u=v-atS={(2v-at)/2}*tS= {v-(1/2)at}*tS=vt-(1/2)at2-Thunder
If the discriminant is greater than zero (b^2 - 4ac) > 0, then the equation have two roots that are real and unequal. Further, the roots are rational if and only if (b^2 - 4ac) is a perfect square, otherwise the roots are irrational.Example:Find the equation whose roots are x = u/v and x = v/uSolution:x = u/vx - u/v = 0x = v/ux - v/u = 0Therefore:(x - u/v)(x - v/u) = (0)(0) or(x - u/v)(x - v/u) = 0Let c = u/v and d = v/u. We can write this equation in equation in the form of:(x - c)(x - d) = 0x^2 - cx - dx + CD = 0 orx^2 - (c +d)x + CD = 0The sum of the roots is:c + d = u/v + v/u = (u)(u)/(v)(u) + (v)(v)/(u)(v) = u^2/uv + v^2/uv = (u^2 + v^2)/uvThe product of the roots is:(c)(d) = (u/v)(v/u) = uv/vu = uv/uv = 1Substitute the sum and the product of the roots into the formula, and we'll have:x^2 - (c +d)x + CD = 0x^2 - [(u^2 + v^2)/uv]x + 1 = 0 Multiply both sides of the equation by uv(uv)[x^2 - ((u^2 + v^2)/uv))x + 1] = (uv)(0)(uv)x^2 - (u^2 + v^2)x + uv = 0 which is the equatiopn whose roots are u/v, v/u
Goof Troop - 1992 O R-V I N-V U 1-8 was released on: USA: 14 September 1992
They're the set of equations that let you link together initial velocity (u), final velocity (v), displacement (s), acceleration (a) and time (t). v=u+ats=ut+(1/2)at^2v^2=u^2+2ass=(1/2)(u+v)ts=vt-(1/2)at^2