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 fardoes the boat travel during this time?​

Answer 1

Correct Question

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s². for 8 s. How fardoes the boat travel during this time?

Solution

A motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3 m/s² for 8 s.

We have to find the distance travelled by the boat.

First equation of motion: v = u + at

Second equation of motion: s = ut + 1/2 at²

Third equation of motion: v² - u² = 2as

From above data we have; initial velocity of the motorboat is 0 m/s, acceleration is 3 m/s² and time taken is 8 sec.

Now, using the Second Equation Of Motion i.e. s = ut + 1/2at²

Substitute the known values,

→ s = 0(8) + 1/2 × 3 × (8)²

→ s = 0 + 3/2 × 64

→ s = 3(32)

→ s = 96

Therefore, the distance covered by the motorboat is 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.