Question

A body travels \( 102.5 \, \text{m} \) in \( n^\text{th} \) second and \( 115.0 \, \text{m} \) in \( (n+2)^\text{th} \) second. The acceleration is:

• A. \( 9 \, \text{m/s}^2 \)
• B. \( 6.25 \, \text{m/s}^2 \)
• C. \( 12.5 \, \text{m/s}^2 \)
• D. \( 5 \, \text{m/s}^2 \)

Answer 1

The Correct Option is B

Formula for Distance Travelled in the nth Second

The distance s_n travelled by a body in the nth second is given by:

s_n = u + (\(\frac{a}{2}\))(2n − 1)

where u is the initial velocity, a is the acceleration, and n is the specific second.

Given Data:
Distance travelled in the nth second: s_n = 102.5 m

Distance travelled in the (n + 2)^th second: s_n+2 = 115.0 m

Using the Formula for the (n + 2)th Second:

s_n+2 = u + $\frac{a}{2}$(2n + 3)

Set Up Equations for s_n and s_n+2:

From the given distances:

102.5 = u + $\frac{a}{2}$(2n − 1)

115.0 = u + $\frac{a}{2}$(2n + 3)

Subtract the First Equation from the Second:

115.0 − 102.5 = (u + $\frac{a}{2}$(2n + 3)) − (u + $\frac{a}{2}$(2n − 1))

12.5 = $\frac{a}{2}$ × 4

12.5 = 2a

a = $\frac{12.5}{2}$ = 6.25 m/s²

Conclusion:

The acceleration of the body is 6.25 m/s².

Answer 2

Step 1: Given data.
The distance travelled in the \( n^{th} \) second, \( s_n = 102.5 \, \text{m} \)
The distance travelled in the \( (n+2)^{th} \) second, \( s_{n+2} = 115.0 \, \text{m} \).

We are asked to find the acceleration \( a \).

Step 2: Formula for distance travelled in the \( n^{th} \) second.
The distance travelled in the \( n^{th} \) second under uniform acceleration is given by: \[ s_n = u + \frac{a}{2}(2n - 1) \] where \( u \) is the initial velocity and \( a \) is the acceleration.

Step 3: Write equations for both cases.
For the \( n^{th} \) second: \[ s_n = u + \frac{a}{2}(2n - 1) = 102.5 \] For the \( (n + 2)^{th} \) second: \[ s_{n+2} = u + \frac{a}{2}[2(n + 2) - 1] = u + \frac{a}{2}(2n + 3) = 115.0 \]
Step 4: Subtract the two equations.
\[ s_{n+2} - s_n = \frac{a}{2}[(2n + 3) - (2n - 1)] = \frac{a}{2}(4) = 2a \] \[ 115.0 - 102.5 = 12.5 = 2a \] \[ \Rightarrow a = 6.25 \, \text{m/s}^2 \]
Step 5: Final Answer.
\[ \boxed{a = 6.25 \, \text{m/s}^2} \]