Question

Question 31:
A motorcyclist starts from rest and reaches a speed of 6 m/s after travelling with uniform acceleration for3s. What is his acceleration ​

Answer 1

Answer :

2 m/s²

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

• Initial velocity (u) = 0 m/s (As it starts from rest)
• Final velocity (v) = 6 m/s
• Time taken (t) = 3s

We are asked to calculate the acceleration.

Basically, here we can find the acceleration in two ways. Firstly, by using the acceleration formula. Secondly, by using the first equation of motion.

Before commencing the steps, let's understand about acceleration. Acceleration is defined as the rate of change in velocity. Its SI unit is m/s². It is vector quantity, that meaning it requires both magnitude and direction for its description.

Now, by using the formula of acceleration :

$\longmapsto \bf { a = \dfrac{v-u}{t}}$

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

$\longmapsto \rm { a = \dfrac{6-0}{3}}$

$\longmapsto \rm { a =\cancel{ \dfrac{6}{3}}}$

$\longmapsto \bf { a = 2 \; m/s^2}$

∴ Acceleration of the motorcyclist is 2 m/s².

$\rule{200}2$

By using the first equation of motion,

$\longmapsto \bf { v = u + at}$

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

$\longmapsto \rm {6 = 0 + 3a}$

$\longmapsto \rm {6 -0 =3a}$

$\longmapsto \rm {6=3a}$

$\longmapsto \rm { \cancel{ \dfrac{6}{3}} = a}$

$\longmapsto \bf { 2 \; m/s^2 = a}$

∴ Acceleration of the motorcyclist is 2 m/s².