Question

A Cyclist rolls down a hill. He starts from rest and after 8s he is travelling at 13.6m/s. What is his acceleration?

Answer 1

Answer :

• Acceleration of the cyclist starting from rest and moving with a Velocity of 13.6 m/s after 8 s is 1.7 m/s².

Explanation :

Given :

• Time taken by the cyclist, t = 8 s
• Final velocity of the cyclist, v = 13.6 m/s
• Initial velocity of the cyclist, u = 0 m/s

[Note : Since the cyclist is starting from rest, the initial velocity of the cyclist will be taken as zero]

To find :

• Acceleration produced by the cyclist, a = ?

Knowledge required :

First equation of motion :

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time Taken

Solution :

By using the first equation of motion and substituting the values in it, we get :

⠀⠀=> v = u + at

⠀⠀=> 13.6 = 0 + a × 8

⠀⠀=> 13.6 = 8a

⠀⠀=> 13.6/8 = a

⠀⠀=> 1.7 = a

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ a = 1.7 m/s²

Therefore,

• Acceleration produced by the cyclist, a = 1.7 m/s²

Answer 2

Explanation:

Acceleration = 1.7 m/s²

$\underline{\bigstar\:\textsf{Given:}}$

• Time (t) = 8 s
• Initial velocity (u) = 0 m/s [starting from rest]
• Final velocity (v) = 13.6 m/s

$\underline{\bigstar\:\textsf{To\:find:}}$

• Acceleration (a) = ?

$\underline{\bigstar\:\textsf{Solution:}}$

Let's take analysis of the situation !

There is a cyclist who rolled down a hill, starting from rest he traveled at a velocity of 13.6 m/s in 8 seconds. Now, we have to calculate the magnitude of acceleration.

Let's find now !

We remember the formula of acceleration i.e,

$\green{\sf{Acceleration\:=\:\dfrac{Final\:velocity\:-\:Initial\:velocity}{Time}}}$

(Now, just put all the given values)

$\implies\:\sf{a\:=\:\dfrac{13.6\:-\:0}{8}}$

$\implies\:\sf{a\:=\:\dfrac{13.6}{8}}$

$\implies\:\sf{a\:=\:1.7\:m/s^2}$

$\sf{\underline{\boxed{\large{\mathsf{\therefore \: His\:acceleration\:is\:1.7\:m/s^2}}}}}$

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》We can find acceleration by Newton's first law of motion also i.e, v = u + at. The ans will be same only.

Hope it helped you dear...