This is a suggested solution for GCE O Level Physics, November, Paper 1, Section A, Question 1.

In this question, it was stated that a stone fell from the top of a cliff to the sea and the following speed-time graph was provided:

(a) The student is required to state how acceleration can be found from a speed-time graph. The suggested answer is as follows:

Acceleration can be found by the gradient of the tangent at a specific point on the curve in the speed-time graph.

(b) In this part b of the question, the student is asked to describe how the acceleration of the stone changes between point A and point D. This part of the question only require the student to describe. Hence by observing from the given speed-time graph and describing his acceleration is all that is required. The suggested answer is as follows:

At point A, when the stone is dropped, its falling speed increases with time and it therefore experience acceleration. However,  the stone experience decreasing acceleration, i.e the rate of increase in speed decreases over time. At point C, there is sudden substantial drop in the speed of the stone, i.e, the stone was experiencing deceleration or retardation until point D. After point D, the stone’s acceleration is zero.

 

(c) In this part of the question, the student is required to explain in terms of the forces acting, why the acceleration changes from point A and B. The suggested answer is as follows:

At point A, when the stone is dropped, the earth’s gravitational force (also known as the weight of the stone) acts on the stone and pulls it towards the centre of the earth. In the free fall motion, the stone’s speed increases at an acceleration of 10ms-2. However, in the presence of air, the air resistance, which is a frictional force that opposes motion, acts on the stone in opposite direction to the gravitational force. As the speed of the falling stone increases, the opposing air resistance (frictional force) also increases to retard the motion. This cause the rate of increase in speed, i.e. the acceleration, to reduce as the stone drops from point A to point B.

 

(d) The student is required to explain from the given speed-time graph that it did not reach terminal velocity in the air.

 

From the graph, there is a steep and sudden drop in its speed at point C. This indicates that point C is the point where the stone hit the sea water. As water has a higher density than air, the opposing frictional force (water resistance) from the water causes a steep retardation to the speed of the stone as shown in the segment of the graph from C to D. Terminal velocity occurs when the opposing frictional force is equal to the weight of the object causing the speed to remain constant (horizontal line on speed-time graph). Since there is no segment on the graph before point C that shows that the speed of the stone remained constant, it means the stone did not reach terminal velocity in the air.

 

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