Question

If the velocity is v=2i+t2j-9k, then the magnitude of the acceleration at t=0.5s is

Answer 1

Answer:

Given;

$\longrightarrow \displaystyle \rm \: v = 2\hat{i} + t^2\hat{j} - 9\hat{k}$

• Instantaneous Acceleration:

The acceleration of an particle at a given instant of time is called as Instantaneous Acceleration.

$\longrightarrow \displaystyle\bold{a = \lim_{\Delta t\to 0 } \frac{ \Delta v}{\Delta t}}$

Or;

$\longrightarrow \displaystyle\bold{a= \dfrac{ d v}{d t}}$

$\longrightarrow \displaystyle \rm{a= \dfrac{ d}{d t}}( 2\hat{i} + {t}^{2} \hat{j} - 9\hat{k})$

$\longrightarrow \displaystyle \rm{a=0 + 2t \hat{j} - 0 }$

$\longrightarrow \displaystyle \bf{a = 2t \hat{j} \: {ms}^{ - 2} }$

At t = 0.5 s the acceleration will be :

$\longrightarrow \displaystyle \rm{a = 2(0.5) \hat{j} \: {ms}^{ - 2} }$

$\longrightarrow \displaystyle \rm{ a= 1 \hat{j} \: {ms}^{ - 2} }$

$\longrightarrow \displaystyle \bf{ | a | = 1 \: {ms}^{ - 2} }$