Question

16. A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 ms 2
for 8 seconds. How far does the boat travel during this time?
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Answer 1

Given :

• Acceleration of boat = 3 m/s²
• Time = 8 seconds

To Find :

• The distance travelled by the boat during that time

Solution :

From second equation of motion ,

$\\ \star \: {\boxed{\sf{\purple{s = ut + \dfrac{1}{2}a {t}^{2} }}}}$

Where ,

• u is initial velocity
• t is time
• a is acceleration
• s is distance travelled

We have ,

• u = 0 [starting from rest]
• t = 8 sec
• a = 8 m/s²

Substituting the values in the equation ,

$\\ : \implies \sf \: s = (0)(8) + \dfrac{1}{2} (3 ) {(8)}^{2}$

$\\ : \implies \sf \: s = \dfrac{1}{2} (3)(64)$

$\\ : \implies \sf \: s = 32 \times 3 \: m$

$\\ : \implies{\underline{\boxed{\pink{\mathfrak{s = 96 \: m}}}}} \: \bigstar$

Hence ,

• The distance travelled by the boat during that time is 96 m.

Answer 2

Answer:

Given :-

• Acceleration of boat = 3 m/s²

• Time = 8 seconds

To Find :-

Distance travelled

Solution :-

Here, we will use Newton second equation

$\small {\boxed {\green { \bf s = ut + \dfrac{1}{2} at {}^{2} }}}$

Here,

s = Distance

U = Initial velocity

T = Time

A = Acceleration

T = Time

$\sf \: s = (0)(8) + \dfrac{1}{2} (3)(8) {}^{2}$

$\sf \: s \: = 0 + \dfrac{1}{2} (3)(64)$

$\sf \: s = 0 + \dfrac{1}{2} \times 32 \times 3$

${\small {\boxed {\orange { \mathfrak {s = 96 \: m}}}}} \bigstar$

The distance travelled by the boat during that time is 96 m.