High School

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If a body with an initial velocity of zero is moving with a uniform acceleration of 8 m/s², the distance traveled by it in the fifth second will be:

A. 36 metres
B. 40 metres
C. 100 metres
D. Zero

Answer :

To find the distance travelled by a body in the fifth second when it starts from rest and moves with uniform acceleration, we use the formula for distance travelled in a specific second:

[tex]s_n = u + \frac{1}{2}a(2n-1)[/tex]

where:

  • [tex]s_n[/tex] is the distance travelled in the [tex]n[/tex]-th second,
  • [tex]u[/tex] is the initial velocity,
  • [tex]a[/tex] is the uniform acceleration,
  • [tex]n[/tex] is the specific second.

Given that:

  • Initial velocity, [tex]u = 0[/tex] m/s (since it starts from rest),
  • Uniform acceleration, [tex]a = 8[/tex] m/s²,
  • We need the distance travelled in the fifth second, so [tex]n = 5[/tex].

Substituting these values into the equation:

[tex]s_5 = 0 + \frac{1}{2} \times 8 \times (2 \times 5 - 1)[/tex]

Simplify the expression inside the parenthesis:

[tex]2 \times 5 - 1 = 10 - 1 = 9[/tex]

Now substitute back:

[tex]s_5 = \frac{1}{2} \times 8 \times 9 = 4 \times 9 = 36~\text{metres}[/tex]

Thus, the distance travelled by the body in the fifth second is [tex]36[/tex] metres.

Therefore, the correct option is [tex]\mathbf{A.}[/tex] 36 metres.

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