Question

(a) Draw velocity-time graph for a body starting its motion with a velocity "u" and under uniform acceleration "a" it acquires a velocity "v" in time "t".
(b) Using above graph, derive second equation of motion for position-velocity relation.
(c) It is possible for an object to move with a constant speed, but with uniform acceleration. Explain.

CBSE Class IX Science LA (5 Marks)

Answer 1

a) image attached
b) Derivation of second equation of motion for position-time relation :Distance travelled, s = area of the trapezium OABCs = 12(area of the triangle ABD) + area of the rectangle OADCor, s = (12× base × height) + ( length × breadth)s = (12× AD × BD) + (OC × OA) ...(1) 1From the figure,AD = OC = tBD = (BC – DC) = (v – u)= (u + at – u) = at OA = u [As v = u + at] 1Putting the above values in equation (1), we get,s = ( 12 × t × at) + (t × u) 1s = ut + 12at2This is the second equation of motion.
c)  A body in a circular path has constant velocity, but as the direction of velocity changes at every point, the acceleration is uniform.

Answer 2

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