Question

Write the three equations of motion. Explain how signs play a role in the applications of these equations.
Derive the formula to find the displacement of an object under uniform acceleration in its $n^{th}$ second.
[5 Marks]

Answer 1

The equations of motion are given by:
$v=u+at$
$s=ut+1/2a{t}^2$
$v^2=u^2+2as$
[1.5 Marks]

These equation have vector quantities involved namely displacement, velocity and acceleration. It has to be ensured that each of these quantities are used with proper signs to get the correct results.
[0.5 Marks]

After (n-1) seconds, displacement is:
$s_{n-1}=u(n-1)+1/2a(n-1^2)...\left(i\right)$
[1 Mark]
After (n) seconds, displacement is:
$s_n=un+1/2a{n}^2...\left(ii\right)$
[1 Mark]

Subtracting (i) from (ii), we get:
$s_n-s_{n-1}=[un+1/2a{n}^2]-\left[u\right(n-1)+1/2a(n-1^2\left)\right]$
$s_n-s_{n-1}=u+1/2a(n^2-(n^2-2n+1\left)\right)$
$s_n-s_{n-1}=u+1/2a(2n-1)$
[1 Mark]