Question 805: [Kinematics > Linear motion] (Past Exam Paper – N89 / I / 2)
A stone, thrown vertically upwards from the ground level, rises to a height h and then falls to its starting point.
Assuming that air resistance is negligible, which of the following graphs best shows how EK, the kinetic energy of the stone, varies with s, the distance travelled?
Solution 805:
Answer: C.
As the stone is thrown up, it is given kinetic energy by the thrower. This kinetic energy is being converted to gravitational potential energy as the ball moves up.
The acceleration due to gravity is downwards. So, the speed of the stone decreases as it moves upward until it becomes zero at the maximum height h.
Kinetic energy, EK = ½ mv2
Gravitational potential energy = mgs
s is the distance travelled.
From the conservation of energy, at any position, this following equation holds.
EK = mgs
Since we are examining the graph of the kinetic energy EK with distance s, we do not need to expand the formula for kinetic energy (EK = ½ mv2)
EK = mgs
We know that, for the upward motion, as s increases, EK decreases. [B is incorrect] The above equation depends only linearly on s (that is the s is not s2 or s3 or …). So the graph should be a straight line. [C is correct]
Initially, when s = 0, EK is maximum.
At the maximum height (s = h), EK = 0.
Then, as the stone falls down again, distance travelled s keeps on increasing but since the stone is now losing height (gravitational potential energy), it gains kinetic energy again.
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