Question

A train travelling at 30 ms -1. accelerates at 0.5ms-1 for 30s. How far will it travel in his time

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Answer 1

Proper question: A train travelling at 30 m/s, accelerates at 0.5 m/s² for 30 s. How far will it travel in this time?

Provided that:

• Initial velocity = 30 m/s
• Acceleration = 0.5 m/s²
• Time taken = 30 seconds

To calculate:

• The distance

Solution:

• The distance = 1125 m

Using concept:

• Second equation of motion

Using formula:

• ${\small{\underline{\boxed{\sf{s \: = ut \: + \dfrac{1}{2} \: at^2}}}}}$

Where u denotes initial velocity, t denotes time taken, a denotes acceleration.

Required solution:

$:\implies \sf s \: = ut \: + \dfrac{1}{2} \: at^2 \\ \\ :\implies \sf s \: = 30(30) + \dfrac{1}{2} \times 0.5(30)^{2} \\ \\ :\implies \sf s \: = 30(30) + \dfrac{1}{2} \times 0.5 \times 30 \times 30 \\ \\ :\implies \sf s \: = 30(30) + \dfrac{1}{2} \times 0.5 \times 900 \\ \\ :\implies \sf s \: = 900 + \dfrac{1}{2} \times 0.5 \times 900 \\ \\ :\implies \sf s \: = 900 + \dfrac{1}{\cancel{{2}}} \times 0.5 \times \cancel{900} \\ \\ :\implies \sf s \: = 900 + 1 \times 0.5 \times 450 \\ \\ :\implies \sf s \: = 900 + 1 \times 225 \\ \\ :\implies \sf s \: = 900 + 225 \\ \\ :\implies \sf s \: = 1125 \: m \\ \\ :\implies \sf Distance \: = 1125 \: metres$