Question

If the distance traveled by a body in the nth second is given by (4 + 6 n) m then find the initial velocity and acceleration of the body.

• A. 6 m $s^{-2}$, 7 m $s^{-1}$
• B. 6 m $s^{-2}$, 3 m $s^{-1}$
• C. 16 m $s^{-2}$, 17 m $s^{-1}$
• D. 26 m $s^{-2}$, 7 m $s^{-1}$

Answer 1

The correct option is A 6 m $s^{-2}$, 7 m $s^{-1}$

$D_{n^{th}sec}=D_{nsec}-D_{(n-1)sec}$

$4+6n=(un+\frac{1}{2}a{n}^2)$$-\left(u\right(n-1)+\frac{1}{2}a(n-1{)}^2)$

$⟹4+6n=u-\frac{1}{2a+an}$

Comparing LHS and RHS

$6n=an$

$⟹a=6m/s^2$

$4=u-\frac{1}{2}a$

$⟹4=u-3$

$⟹4=4+3=7m/s$