Question

A body sliding down on a smooth inclined plane slides 1/4th distance in 2 s. It will

slide down the complete plane in how many seconds??​

Answer 1

Given

Time taken to slide down 1/4th of a slope is 2 s

To find

Time taken to slide down the complete plane

Solution

Let s be the distance to slide down the complete plane.

a = Acceleration

For 1/4th distance t = 2

$\dfrac{s}{4}=ut+\dfrac{1}{2}at^2\\\Rightarrow \dfrac{s}{4}=\dfrac{1}{2}a2^2\\\Rightarrow \dfrac{s}{4}=2a\\\Rightarrow s=8a$

For complete plane t = ?

$s=0t+\dfrac{1}{2}at^2\\\Rightarrow s=\dfrac{1}{2}at^2$

So

$8a=\dfrac{1}{2}at^2\\\Rightarrow 16=t^2\\\Rightarrow t=4\ \text{s}$

Hence, time taken to slide down the complete plane is 4 seconds.

Answer 2

Explanation:

Given

Time taken to slide down 1/4th of a slope is 2 s

To find

Time taken to slide down the complete plane

Solution

Let s be the distance to slide down the complete plane.

a = Acceleration

For 1/4th distance t = 2

\begin{gathered}\dfrac{s}{4}=ut+\dfrac{1}{2}at^2\\\Rightarrow \dfrac{s}{4}=\dfrac{1}{2}a2^2\\\Rightarrow \dfrac{s}{4}=2a\\\Rightarrow s=8a\end{gathered}

4

s

=ut+

2

1

at

2

⇒

4

s

=

2

1

a2

2

⇒

4

s

=2a

⇒s=8a

For complete plane t = ?

\begin{gathered}s=0t+\dfrac{1}{2}at^2\\\Rightarrow s=\dfrac{1}{2}at^2\end{gathered}

s=0t+

2

1

at

2

⇒s=

2

1

at

2

at

2

⇒16=t

2

⇒t=4 s

Hence, time taken to slide down the complete plane is 4 seconds.