Question

a motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3m/s for 8 sec.how far does the boat travel during this time

Answer 1

Ans:3m

v=u+at

=>v=at

=>a=v/t=3/8m/s^2.

Now,

v^2=u^2+2as

=>v^2=2as

=>s=v^2/2a=(3×3)/{2×(3/8)}=9/3=3.

Hence s=3m

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.l