Question

A motorboat started from rest on a lake accelerates in a straight line at a constant rate of 3.0ms-2 for 8.0s. How far the boat travel during this time

Answer 1

$\large{\bf{\gray{\underline{\underline{\orange{Given:}}}}}}$

Initial velocity = zero

Acceleration = 3m/s²

Time of journey = 8s

$\large{\bf{\gray{\underline{\underline{\green{To\:Find:}}}}}}$

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

$\large{\bf{\gray{\underline{\underline{\pink{Solution:}}}}}}$

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

Let's apply 2nd eq. of kinematics :

$:\implies\tt\:s=ut+\dfrac{1}{2}at^2$

$:\implies\tt\:s=(0\times t)+\dfrac{1}{2}(3\times 8^2)$

$:\implies\tt\:s=\dfrac{1}{2}(192)$

$:\implies\boxed{\bf{\red{s=96\:m}}}$

Answer 2

Given ,

Initial velocity (u) = 0 m/s

Acceleration (a) = 3 m/s²

Time (t) = 8 sec

We know that , the Newton's second equation of motion is given by

$\boxed{ \sf{s = ut + \frac{1}{2}a {(t)}^{2} }}$

Thus ,

s = 0 × 8 + 1/2 × 3 × (8)²

s = 3/2 × 64

s = 3 × 32

s = 96 m

∴ The boat will travel 96 m in given time period