Question

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

Answer 1

Answer:

96m

Explanation:

We know the equation of motion

Distance, s=ut + (1/2)at2 —————-(i)

Substituting the given and known values in equation (i) we get,

s= o (8) + 1/2 (3) (8)2

= 1/2 (3) (64) { 82 = 8 X 8=64}

= 3 (32)

= 96

Therefore, The distance travel by motorboat = 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.