Question

A motorboat starting from rest on a on a lake accelerated in a straight line at a constant rate of 3 metre per second square for 2 minutes the distance travelled by the boat during the time will be

option


8m 4m 28.8m 14.4m

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Answer 1

Answer:

Provided that:

• Initial velocity = 0 mps
• Acceleration = 3 mps sq.
• Time = 2 minutes

To calculate:

• Distance travelled

Solution:

• Distance travelled = 21600 m

Using concepts:

• Second equation of motion
• Formula to convert min-sec

Using formulas:

• Second equation of motion:

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

• Formula to convert min-sec:

• ${\small{\underline{\boxed{\pmb{\sf{1 \: min \: = 60 \: seconds}}}}}}$

Where, s denotes displacement or distance or height, u denotes initial velocity, t denotes time taken and a denotes acceleration.

Required solution:

~ Firstly let us convert min-sec!

»»» 1 min = 60 seconds

»»» 2 min = 2 × 60 seconds

»»» 2 min = 120 seconds

• Henceforth, converted!

~ Now let us find out the distance travelled by using second equation of motion!

$:\implies \sf s \: = ut \: + \dfrac{1}{2} \: at^2 \\ \\ :\implies \sf s \: = 0(120) + \dfrac{1}{2} \times 3(120)^{2} \\ \\ :\implies \sf s \: = 0 + \dfrac{1}{2} \times 3 \times 14400 \\ \\ :\implies \sf s \: = \dfrac{1}{2} \times 3 \times 14400 \\ \\ :\implies \sf s \: = 1 \times 3 \times 7200 \\ \\ :\implies \sf s \: = 21600 \: m \\ \\ :\implies \sf Distance \: = 21600 \: m$

• Dear user according to the calculations this answer is correct except of given options.