Starting from the displacement–time relation for uniform acceleration

PHYSICS · Subjective · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Starting from the displacement–time relation for uniform acceleration,

s = ut + \tfrac12 gt^2,

answer the following: (a) Rearrange the equation to obtain an explicit expression for the initial velocity

u

in terms of

s

t

and

g

. (b) Show that when the body is simply dropped (i.e.

u=0

), your expression reduces to the familiar formula

s = \tfrac12 gt^2

. (c) A stone is thrown vertically downward and covers 30\,m in 2.0\,s. Use the expression derived in part (a) to find its initial speed.