Question

A particle is moving with a velocity of 10 m/s towards east. After 10 s its velocity changes to 10 m/s towards north. Its average
acceleration is​

Answer 1

Given :

Initial velocity = 10 i m/s

Final velocity = 10 j m/s

Time interval = 10s

To Find :

Acceleration of particle.

Solution :

❇ Acceleration is defined as the rate of change of velocity

• It is a vector quantity having both magnitude as well as direction.
• It can be positive, negative or zero.
• SI unit : m/s²

In this question, magnitude and direction both are changes. So first of all we need to find magnitude of change in velocity.

$:\implies\sf\:\Delta v=\sqrt{(10)^2+(10)^2}$

$:\implies\sf\:\Delta v=\sqrt{100+100}$

$:\implies\sf\:\Delta v=\sqrt{200}$

$:\implies\bf\:\Delta v=10\sqrt{2}\:m/s$

Now as per definition acceleration;

$:\implies\sf\:a=\dfrac{\Delta v}{\Delta t}$

$:\implies\sf\:a=\dfrac{10\sqrt2}{10}$

$:\implies\sf\:a=\sqrt2$

$:\implies\:\underline{\boxed{\bf{\purple{a=1.41\:ms^{-2}}}}}$