Question

Q.9: A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 ms for 8 s. How far
does the boat travel during this time?
​

Answer 1

Given, initial velocity of boat is: u=0

Acceleration is: a=3 ms  

−2

 

Time is: t=8 s

Using second equation of motion:

s=ut+  

2

1

​  

at  

2

 

s=0×8+  

2

1

​  

×3×8  

2

=96 m.

Answer 2

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.