(a) Distinguish between perfectly elastic collision and perfectly inelastic collision.
(b) Sketch a distance — time graph for a particle moving in a straight line with:
(i) uniform speed;
(ii) variable speed.
(c) A body starts from rest and travels distances of 120, 300 and 180m in successive equal time intervals of 12 s. During each interval the body is uniformly accelerated. (i) Calculate the velocity of the body at the end of each successive time interval.
(ii) Sketch a velocity-time graph for the motion.
(b) Sketch a distance — time graph for a particle moving in a straight line with:
(i) uniform speed;
(ii) variable speed.
(c) A body starts from rest and travels distances of 120, 300 and 180m in successive equal time intervals of 12 s. During each interval the body is uniformly accelerated. (i) Calculate the velocity of the body at the end of each successive time interval.
(ii) Sketch a velocity-time graph for the motion.
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Correct Answer: Option n
Explanation:
(b)
(c)(i) Stage 1; S = ut + \(\frac{1}{2}at^2\)
= 120 = 0 x 12 + \(\frac{1}{2}\) x a x 12\(^2\)
a = \(\frac{5}{6}\)
\(V_1 = u + at\)
= 20 + \(\frac{5}{6} \times 12 = 30m/s\)
Stage 3; S = ut + \(\frac{1}{2}\) at\(^2\)
-180 = 30 x 12v + \(\frac{1}{2}\) x a x 12\(^2\)
a = \(\frac{-5}{2}\)
V\(_3\) = u + at = 30 + \(\frac{-5}{2}\) x 12 = 0m/s
(ii) v/m\(^{s - 1}\)
| Perfectly Elastic | Perfectly Inelastic |
| K.E. is conservedColliding objects do not stick together after collisionIn case of head-on collision directions of the bodies are reversed | K.E. decreasesColliding objects stick and move together after collisionDirection of both bodies may or may not be reserved |
(b)
(c)(i) Stage 1; S = ut + \(\frac{1}{2}at^2\)
= 120 = 0 x 12 + \(\frac{1}{2}\) x a x 12\(^2\)
a = \(\frac{5}{6}\)
\(V_1 = u + at\)
= 20 + \(\frac{5}{6} \times 12 = 30m/s\)
Stage 3; S = ut + \(\frac{1}{2}\) at\(^2\)
-180 = 30 x 12v + \(\frac{1}{2}\) x a x 12\(^2\)
a = \(\frac{-5}{2}\)
V\(_3\) = u + at = 30 + \(\frac{-5}{2}\) x 12 = 0m/s
(ii) v/m\(^{s - 1}\)