Question

An object is moving in a straight line with constant acceleration. It covers 65 m distance in 5th second and 105 m distance in 9th second. The distance covered by it in 20 seconds is

• A. 240 m
• B. 2040 m
• C. 2400 m
• D. 2004 m

Answer 1

The correct option is C

2400 m

Step 1: Given:

An object moving with a constant acceleration, $a$

Distance covered by it in 5th second $=65m$

Distance covered by it in 9th second $=105m$

Step 2: Finding the equations of motion of the object in the $n^{th}$ second:

We know that the distance covered in nth second is given by $S_n=u+\frac{a}{2}(2n-1)$ where $u$ and $a$ are the initial velocity and acceleration respectively.

Case 1:

$$\begin{gathered} S_n=65 \\ n=5secs \\ so,65=u+\frac{a}{2}(2\times 5-1) \\ Weget65=u+4.5a.....\left(1\right) \end{gathered}$$

Case 2:

$$\begin{gathered} S_n=105 \\ n=9secs \\ so,105=u+\frac{a}{2}(2\times 9-1) \\ Weget105=u+8.5a.....\left(2\right) \end{gathered}$$

Step 3: Finding the initial velocity of the object, u:

Subtracting equation (1) from equation (2), we get

$$\begin{gathered} 40=4aora=10m/s^2 \\ So,65=u+4.5\times 10 \\ ⟹u=20m/s \end{gathered}$$

Finding the distance covered by the object in 20 seconds:

$$\begin{gathered} Dis\tan cecoveredin20secondsisgivenby \\ S=ut+\frac{1}{2}a{t}^{2}wheret=20s \\ S=20\times 20+\frac{1}{2}\left(10\right){\left(20\right)}^2 \\ =2400m \end{gathered}$$

Therefore, the object covers 2400 m in 20 seconds.

Hence, the correct answer is (C) 2400 m.