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Physics

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AREAS

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DEFINITE INTEGRALS LEVEL - 1

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Pdf Description

Page 1 :

1 | Short Formula (Physics), , SHORT FORMULA, PHYSICS, , UNIT AND DIMENSIONS, Unit :, Measurement of any physical quantity is expressed in terms of an internationally accepted certain, basic standard called unit, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , * Fundamental Units., S.No. Physical Quantity SI Unit Symbol, 1 Length Metre m, 2 Mass Kilogram Kg, 3 Time Second Ss, 4 Electric Current Ampere A, 5 Temperature Kelvin K, 6 Luminous Intensity Candela Cd, 7 Amount of Substance Mole mol, . Supplementary Units :, S.No. Physical Quantity SI Unit Symbol, 1 Plane Angle radian r, 2 Solid Angle Steradian Sr

1 | Short Formula (Physics), , SHORT FORMULA, PHYSICS, , UNIT AND DIMENSIONS, Unit :, Measurement of any physical quantity is expressed in terms of an internationally accepted certain, basic standard called unit, , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , , * Fundamental Units., S.No. Physical Quantity SI Unit Symbol, 1 Length Metre m, 2 Mass Kilogram Kg, 3 Time Second Ss, 4 Electric Current Ampere A, 5 Temperature Kelvin K, 6 Luminous Intensity Candela Cd, 7 Amount of Substance Mole mol, . Supplementary Units :, S.No. Physical Quantity SI Unit Symbol, 1 Plane Angle radian r, 2 Solid Angle Steradian Sr

Page 2 :

| Short Formula (Physics), *, , Metric Prefixes :, , , , , , , , , , , , , , , , , , , , S.No. Prefix Symbol Value, 1 Centi c 10", 2 Mili m 10", 3 Micro u 10®, 4 Nano n 10*, 5 Pico Pp 10", 6 Kilo K 10®, 7 Mega M 10°, , , , , , , , , , , , Average Velocity (in an interval) :, , = — _ Total displacement _, v= = <ve =, Total time taken, , , , Average Speed (in an interval), , Total distance travelled, , ‘Average Spesd'= Total time taken, , Instantaneous Velocity (at an instant) :, , Ar, v,. = lim —, inst ~ at 0 At, , Average acceleration (in an interval):, , AV Mem, , At At, , Instantaneous Acceleration (at an instant):, , “AV, = lim, , 2 moe AL, , a, dt

| Short Formula (Physics), *, , Metric Prefixes :, , , , , , , , , , , , , , , , , , , , S.No. Prefix Symbol Value, 1 Centi c 10", 2 Mili m 10", 3 Micro u 10®, 4 Nano n 10*, 5 Pico Pp 10", 6 Kilo K 10®, 7 Mega M 10°, , , , , , , , , , , , Average Velocity (in an interval) :, , = — _ Total displacement _, v= = <ve =, Total time taken, , , , Average Speed (in an interval), , Total distance travelled, , ‘Average Spesd'= Total time taken, , Instantaneous Velocity (at an instant) :, , Ar, v,. = lim —, inst ~ at 0 At, , Average acceleration (in an interval):, , AV Mem, , At At, , Instantaneous Acceleration (at an instant):, , “AV, = lim, , 2 moe AL, , a, dt

Page 3 :

| Short Formula (Physics), , Graphs in Uniformly Accelerated Motion along a straight line (a 0), x is a quadratic polynomial in terms of t. Hence x — t graph is a parabola., , ‘a<0, % x, a>0, 3 3, x-t graph, vis a linear polynomial in terms of t. Hence v-t graph is a straight line of slope a., v v, 22, g uh Sy, SR Pe., s @, u, ais positive, | ais negative,, > ooo, , oJ, 2, , v-t graph, , a-t graph is a horizontal line because a is constant., , , , , , a a, positive, acceleration, arr gt, negative, i a |_acceleration, aj)? 1 <aceeeratic, 0}, a-t graph, Maxima & Minima, dy dy i dy qd gy 3, x = Bax dx <Oat maximum and dx “08a, & «7 Oat minima., , Equations of Motion (for constant acceleration), (a) veutat, , (b) o=utt 3 at sevi- 5 att Kextutt > att, (c) vi=u® +2as, , @ s-4%,, , (e) s,=u+ 5 (2n-1), , For freely falling bodies : (u = 0)

| Short Formula (Physics), , Graphs in Uniformly Accelerated Motion along a straight line (a 0), x is a quadratic polynomial in terms of t. Hence x — t graph is a parabola., , ‘a<0, % x, a>0, 3 3, x-t graph, vis a linear polynomial in terms of t. Hence v-t graph is a straight line of slope a., v v, 22, g uh Sy, SR Pe., s @, u, ais positive, | ais negative,, > ooo, , oJ, 2, , v-t graph, , a-t graph is a horizontal line because a is constant., , , , , , a a, positive, acceleration, arr gt, negative, i a |_acceleration, aj)? 1 <aceeeratic, 0}, a-t graph, Maxima & Minima, dy dy i dy qd gy 3, x = Bax dx <Oat maximum and dx “08a, & «7 Oat minima., , Equations of Motion (for constant acceleration), (a) veutat, , (b) o=utt 3 at sevi- 5 att Kextutt > att, (c) vi=u® +2as, , @ s-4%,, , (e) s,=u+ 5 (2n-1), , For freely falling bodies : (u = 0)

Page 5 :

| Short Formula (Physics), , Vag(velocity of A with respect to B) =v, -Vg, , Ag (acceleration of A with respect to B) = a, —ag, , Relative motion along straight line - x,,=x, Xy, , CROSSING RIVER, A boat or man in a river always moves in the direction of resultant velocity of velocity of boat (or man) and, velocity of river flow., , 1. Shortest Time :, Velocity along the river, v, =v., Velocity perpendicular to the river, v,= Vig, , i 2, mk + VR, , , , The net speed is given by v,,, , , , 2. Shortest Path :, velocity along the river, v,,=0 y, , 1, , 1, , , , and velocity perpendicular to river Va 4 2 va 1B, X, , , , , , The net speed is given by v, = 2 jz 4 *, v,, at an angle of 90° with the river direction. ", velocity v, is used only to cross the river, Vie \O1V en, — x, d A, , therefore time to cross the river, t, , , , = 2, mR — VR, , and velocity v, is zero, therefore, in this case the drift should be zero., , , , , , Vag Vag Sin 0 = 0 or Va = Vag Sin 0, or o=sint SR, VR, RAIN PROBLEMS, Vem = VR Vn or, 1. From third law of motion, , Fas =—Fea Fag = Force onAdue toB Fea = Force on B due toA

| Short Formula (Physics), , Vag(velocity of A with respect to B) =v, -Vg, , Ag (acceleration of A with respect to B) = a, —ag, , Relative motion along straight line - x,,=x, Xy, , CROSSING RIVER, A boat or man in a river always moves in the direction of resultant velocity of velocity of boat (or man) and, velocity of river flow., , 1. Shortest Time :, Velocity along the river, v, =v., Velocity perpendicular to the river, v,= Vig, , i 2, mk + VR, , , , The net speed is given by v,,, , , , 2. Shortest Path :, velocity along the river, v,,=0 y, , 1, , 1, , , , and velocity perpendicular to river Va 4 2 va 1B, X, , , , , , The net speed is given by v, = 2 jz 4 *, v,, at an angle of 90° with the river direction. ", velocity v, is used only to cross the river, Vie \O1V en, — x, d A, , therefore time to cross the river, t, , , , = 2, mR — VR, , and velocity v, is zero, therefore, in this case the drift should be zero., , , , , , Vag Vag Sin 0 = 0 or Va = Vag Sin 0, or o=sint SR, VR, RAIN PROBLEMS, Vem = VR Vn or, 1. From third law of motion, , Fas =—Fea Fag = Force onAdue toB Fea = Force on B due toA

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