Question

A motor boat starting from rest on a lake accelerates in
a straight line at a constant rate of 3.0m/s for 8.0 Seconds. How far does the boat travel during this time?​

Answer 1

Given :

• A boat accelerates at a constant rate of 3 m/s² for 8 seconds .

To Find :

• Distance travelled by the boat during the given time .

Solution :

$\longmapsto\tt{Acceleration\:(a)=3m/{s}^{2}}$

$\longmapsto\tt{Initial\:Velocity\:(u)=0\:m/s}$

$\longmapsto\tt{Time\:Taken\:(t)=8\:sec}$

Using Equation :

$\longmapsto\tt\boxed{s=ut+\dfrac{1}{2}\:a{t}^{2}}$

Putting Values :

$\longmapsto\tt{s=0\times{8}+\dfrac{1}{2}\times{3}\times{{(8)}}^{2}}$

$\longmapsto\tt{s=0+\dfrac{1}{{\cancel{2}}}\times{3}\times{{\cancel{64}}}}$

$\longmapsto\tt{s=3\times{32}}$

$\longmapsto\tt\bf{s=96\:m}$

So , The distance travelled by the motor boat is 96 m .

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Three Equations Of Motion :

• v = u + at
• s = ut + 1/2 at²
• v² - u² = 2as

Here :

• v = Final Velocity
• u = Initial Velocity
• t = Time Taken
• a = Acceleration
• s = Distance Travelled

_______________________

Answer 2

Given :-

A motor boat starting from rest on a lake accelerates in

a straight line at a constant rate of 3.0m/s for 8.0 Seconds.

To Find :-

Distance covered

Solution :-

We know that

s = ut + 1/2 × at²

s = 0 × 8 + 1/2 × 3 × (8)²

s = 0 + 1/2 × 3 × 64

s = 0 + 3 × 32

s = 96 m

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