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Chapter 2: Problem 191

A body starts its motion with zero velocity and its acceleration is $\left(3 \mathrm{~m} / \mathrm{s}^{2}\right)$. Find the distance travelled by it in fifth second. (A) \(15.5 \mathrm{~m}\) (B) \(17.5 \mathrm{~m}\) (C) \(13.5 \mathrm{~m}\) (D) \(14.5 \mathrm{~m}\)

Short Answer

Expert verified
The distance traveled by the body in the fifth second is \(13.5 \mathrm{~m}\), which corresponds to answer (C).

Step by step solution

01

Write down the given data and formula

The given data in the problem are: Initial velocity (u) = 0 m/s Acceleration (a) = 3 m/s² To find the distance traveled in a certain duration, we can use the formula: Distance (s) = u*t + 0.5*a*t²
02

Find the total distance traveled in five seconds

Using the formula in step 1, we can find the total distance traveled in five seconds: s₁ = 0*(5) + 0.5*(3)*(5²) Calculate the value of s₁: s₁ = 0 + 0.5*(3)*(25) s₁ = 37.5 m
03

Find the distance traveled in first four seconds

Now, we will find the distance traveled in the first four seconds: s₂ = 0*(4) + 0.5*(3)*(4²) Calculate the value of s₂: s₂ = 0 + 0.5*(3)*(16) s₂ = 24 m
04

Calculate the distance traveled in the fifth second

To find the distance traveled in the fifth second, we will subtract the distance traveled in first four seconds from the total distance traveled in five seconds: Distance in fifth second = s₁ - s₂ = 37.5 m - 24 m Calculate the value: Distance in fifth second = 13.5 m So, the distance traveled by the body in the fifth second is 13.5 m, which corresponds to answer (C).

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