A small object, of mass 0.02 kg , is dropped from rest from the top of a building which is 160 m high.
Calculate the speed of the object as it hits the ground.
Determine the time taken for the object to reach the ground.
State one assumption you have made in your solution.
The diagram below shows two particles \(A\) and \(B\), of mass 2 kg and 5 kg respectively, which are connected by a light inextensible string passing over a fixed smooth pulley. Initially, \(B\) is held at rest with the string just taut. It is then released.
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Calculate the magnitude of the acceleration of \(A\) and the tension in the string.
What assumption does the word 'light' in the description of the string enable you to make in your solution?
A particle \(P\), of mass 3 kg , moves along the horizontal \(x\)-axis under the action of a resultant force \(F \mathrm {~N}\). Its velocity \(v \mathrm {~ms} ^ { - 1 }\) at time \(t\) seconds is given by
$$v = 12 t - 3 t ^ { 2 }$$
Given that the particle is at the origin \(O\) when \(t = 1\), find an expression for the displacement of the particle from \(O\) at time \(t \mathrm {~s}\).
Find an expression for the acceleration of the particle at time \(t \mathrm {~s}\).