Question

a motorboat starting from rest on a lake accelerates in a straight line at a constant rate of3.0ms^-2for 8.0s.How far does the boat travel during this time?oy



answer this question immediately



tell me correct answer​

Answer 1

Answer:

Distance travelled by the boat is 96 m.

Explanation:

Given:

u = 0 m/s

a = 3 m/s²

t = 8 s

To find:

s = ?

Solution:

According to the 3rd equation of motion,

$\sf{s = ut + \dfrac{1}{2}at^{2} }$

Substituting the values,

$\sf{s = 0 \times 8 + \dfrac{1}{\not 2} \times 3 \times \not 8 \; ^{^{\big 4}} \times 8}$

$\sf{s = 0 + 3 \times4 \times 8}$

$\sf{s = 96}$

Hence,

s = 96 m

Equations of motion:

• $\sf{v = u + at}$

• $\sf{s = ut + \dfrac{1}{2}at^{2} }$

• $\sf{v^{2} - u^{2} = 2as }$

Where,

u = initial velocity

v = final velocity

a = acceleration

s = distance travelled

t = time taken

Answer 2

Answer :

• The boat travels 96 m in 8 seconds

Given :

• Initial velocity of the motorboat = 0 m/s [As it was initially at rest so, it's initial velocity will be zero.]

• Acceleration = 3.0 m/s²

• Time = 8.0 seconds

To find :

• Distance travelled by the motorboat in 8 seconds

Concept :

Here, we have to find the distance travelled by the motorboat in 8 seconds. We can get the required answer by two methods.

FIRST METHOD :-

Firstly, calculate the final velocity of the motorboat by using the first equation of motion. Then to find the distance travelled, use the third equation of motion.

SECOND METHOD :-

To find the distance travelled by the motorboat, use the second equation of motion.

First equation of motion :-

• v = u + at

Second equation of motion :-

• s = ut + ½ at²

Third equation of motion :-

• v² - u² = 2as

where,

• v denotes the final velocity

• u denotes the initial velocity

• t denotes the time taken

• s denotes the distance/displacement

• a denotes the acceleration

Solution :

Solving by using the first method ::

Calculating the final velocity of the motorboat :-

→ First equation of motion :-

→ v = u + at

→ Substituting the given values :-

→ v = 0 + (3)(8)

→ v = 3 × 8

→ v = 24

→ The value of v = 24

Therefore, the final velocity of the motorboat = 24 m/s

Now, calculating the distance travelled :-

→ Third equation of motion :-

→ v² - u² = 2as

→ Substituting the given values :-

→ (24)² - (0)² = 2(3)(s)

→ (24)² = 6 × s

→ 24 × 24 = 6 × s

→ (24 × 24)/6 = s

→ 24 × 4 = s

→ 96 = s

→ The value of s = 96

Therefore, the distance travelled by the motorboat in 8 seconds = 96 m

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━

Solving by using the second method :-

→ Second equation of motion :-

→ s = ut + ½ at²

→ Substituting the given values :-

→ s = (0)(8) + ½ (3)(8)²

→ s = 0 + ½ × 3 × 8 × 8

→ s = ½ × 3 × 8 × 8

→ s = 3 × 4 × 8

→ s = 96

→ The value of s = 96

Therefore, the distance travelled by the motorboat in 8 seconds = 96 m