At what point on this position-time graph is the instantaneous velocity equal to zero?
1. A'
2. B
3. E
4. D
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The correct answer is D.
The instantaneous velocity of a body is given by the gradient of the tangent drawn to the point in the position- time graph.
The tangents drawn to points A and B slopes upwards and thus have a positive gradient, showing that the particle has velocity in the positive direction.
The tangent drawn to point E slopes down wards and hence its gradient is negative. The velocity of the particle is also finite at E, but in opposite direction to that at A and B.
However, point D lies at the top of the peak in the position- time graph. A tangent drawn to the point D is flat and parallel to the time axis. The gradient of the tangent is zero, implying that the velocity of the [article at D is zero.
Thus, from the position- time graph, it can be seen that the velocity of the article at D is zero.