Question

Motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 metre per second for 8.0 second of a does the boat travel during this time.

Answer 1

Answer :

Initial velocity = zero

Acceleration = 3m/s²

Time interval = 8s

We have to find distance covered by motorboat in the given interval of time$.$

Since acceleration of motorboat is said to be constant throughout the motion, we can apply equation of kinematics to solve this question.

Second equation of kinematics is given by

• d = ut + 1/2 at²

d denotes distance

u denotes initial velocity

t denotes time

a denotes acceleration

By substituting the given values,

➝ d = ut + 1/2 at²

➝ d = (0)(8) + 1/2(3)(8)²

➝ d = 0 + 1/2(3)(64)

➝ d = 32 × 3

➝ d = 96 m

∴ Motorboat will cover 96 m distance during the given interval of time.

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.