Force and motion ( Nepali course) Easily explained class 9

Relation between Wera and for first equation. V

3. Let us assume a body has initial velocity 'u' and it is subjected to a uniform Leeleration 'a' so that the final velocity be 'v' after a time interval 't. Now, by the definition of acceleration, we have a = (V - U)/t or, at = v - u (v = u + at)/i (i)

b. Relation between s, u, v and t or second equation Let us assume a body is moving with an initial velocity 'u'. Let after time 't', its

velocity becomes 'v' and the distance travelled by the body be 's'. For uniformly accelerated motion, average velocity is the mean of initial and final velocities. Therefore, we have AV = (u + v)/2 AV = S/t (1) velocity is also calculated by: (2) equation (1) and (2) = (u + v)/2 = s/t or, 2s = (u + v) * t s = (u + v)/2 * t (ii)

c. Relation between s, u, a and t or third equation

Let us assume a body moving with an initial velocity 'u'. Let its final velocity 'v' after a time interval 't' and the distance travelled by the body be 's' then, we already have, v = u + at (i) s = (u + v)/2 * 1 ............... (ii) value of v from the equation (i) in the equation (ii), we have
s = (11 ^ 2 * (n + beta*t))/2 * t 2 s = (2nt)/2 + (n * t ^ 3)/2 s = omega*t + 1/2 * a * t ^ 2 \ . v = a + at \ (im)

d. Relation between u, v, a and s or fourth equation Let us assume a body moving with an initial velocity 'u'. Let its final velocity

after a time Tand the distance travelled by v = u + at s = (it + v)/2 * t (1) value of 't from (i) in the equation (ii) s = (U + v)/2 * (V - U)/(i!) or s = (v ^ 2 - u ^ 2)/(2a) or 2as = v ^ 2 - u ^ 2 v ^ 2 = u ^ 2 + 2as the body be 's'. We already ha v = u + at or (at = v - u)/(t - (v - u)/a) or (ii) (iv)

Application of equations of motion in different situations

Case 1 For a body moving with a uniform velocity, initial velocity (u) - final velocity Hence, acceleration underline (a) = 0 , Therefore, from the equation (iii), we have s = uut + 1/2 * a * t ^ 2 s-ut (- 1/2 * a * t ^ 2 = 0) Case 2. For a freely falling body under gravity a = g and s = h ) equations (i), (ii), ( and (iv) are respectively written as, v=u+at s= sqcup+v 2t \mathfrak{n} = ut + 1/2 * a * t ^ 2 v ^ 2 + u ^ 2 + 2as v = u + gt h = (u + v)/2 * t h = mu*t + 1/2 * g * t ^ 2 v ^ 2 = u ^ 2 + 2gh ⇒ ⇒ ⇒

Notice that in case 2 is replaced by and by h in equations given aboss Here, a negative sign is assigned to if the body is thrown vertically upward. Tha acceleration due to the gravity (g) is oppositely directed te. motion is directel vertically upwards but g is directed vertically downwards.

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