Question

Distance travelled in nth second has the units of

• A. displacement
• B. velocity
• C. acceleration
• D. momentum

Answer 1

Answer: (B)

velocity

Displacement formula for motion

$S=ut+\frac{1}{2}a{t}^2$

displacement after n seconds

$S_n=u{t}_n+\frac{1}{2}a{t_n}^2$

Displacement after (n-1) seconds

$S_{n-1}=u{t}_{n-1}+\frac{1}{2}a{t_{n-1}}^2$

Displacement in $n^{th}$ second is

$s_{n^{th}}=s_n-s_{n-1}$

$⟹S_{n^{th}}=u{(t}_{n-1}-t_n)+\frac{1}{2}a({t_{n-1}{-t}_{n-1})}^2$

because ${(t}_{n-1}-t_n)=1$

Dimension of the $S_{n^{th}}$ is $m/s$