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A body moves from rest with a uniform acceleration and travels 270 m in 3 s. Find the velocity of the body at 10 s after the start.

Motion in One Dimension

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Answer

As we know,

S = ut + 12\dfrac{1}{2} at2

Given,

u = 0 m s -1

S = 270 m

t = 3 s

Substituting the values in the formula above we get,

270=(0×3)+(12×a×32)270=92×a270×2=9×a⇒a=5409⇒a=60ms−2270 = (0 \times 3) + (\dfrac{1}{2} \times a \times 3^2) \\[0.5em] 270 = \dfrac{9}{2} \times a \\[0.5em] 270 \times 2 = 9 \times a \\[0.5em] \Rightarrow a = \dfrac{540}{9} \\[0.5em] \Rightarrow a = 60 \text{ms}^{-2}

Hence, a = 60 m s-2

To find out velocity after t = 10 s.

v = u + at

Substituting the values in the formula above we get,

v=0+(60×10)⇒v=600ms−1v = 0 + (60 \times 10) \\[0.5em] \Rightarrow v = 600 \text{ms}^{-1} \\[0.5em]

Hence, velocity after 10 s = 600 m s-1

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