Question

a motorboat starting from rest on a lake accelerates in a straight line at a constant rate of 3.0 m s-² for 8.0 s. How far does the boat travel during this time?​

Answer 1

Answer:

96 m

Explanation:

As per the provided information in the given question, we have :

• Initial velocity (u) = 0 m/s [As it starts from rest.]
• Acceleration (a) = 3 m/s²
• Time taken (t) = 8 seconds

We've been asked to calculate the distance covered by the boat during this time.

Here, we'll use the 2nd equation of the motion :

$\bigstar \quad\underline{\boxed { \pmb{\frak{s}} = \pmb{\frak{ut}} + \dfrac{\pmb{\frak{1}}}{\pmb{\frak{2}}}\pmb{\frak{at}}^{\pmb{\frak{2}}} }}$

• s denotes distance
• u denotes initial velocity
• a denotes acceleration
• t denotes time

$\longrightarrow \sf{\quad { s = 0(8) + \dfrac{1}{2}\times 3 \times (8)^2 \; m}}$

$\longrightarrow \sf{\quad { s = \dfrac{1}{2}\times 3 \times 64 \; m}}$

$\longrightarrow \sf{\quad { s = 1 \times 3 \times 32 \; m}}$

$\longrightarrow \quad\underline{\boxed { \pmb{\frak{s = 96 \; m}}}}$

Therefore, it travels 96 m during this time.

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Learn More :

Equations of motion :

$\boxed{ \begin{array}{cc} \pmb{\sf{ \quad \: v = u + at \quad}} \\ \\ \pmb{\sf{ \quad \: s= ut + \cfrac{1}{2}a{t}^{2} \quad \: } } \\ \\ \pmb{\sf{ \quad \: {v}^{2} - {u}^{2} = 2as \quad \:}}\end{array}}$

• v denotes final velocity
• u denotes initial velocity
• a denotes acceleration
• t denotes time
• s denotes distance

Answer 2

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