Question

The displacement of a particle moving along x axis is given by x= 18 t, its
velocity and acceleration at t=2s
(a) 36m/s, 18m/s2
(b) 18m/s,Om/s2
(c) Om/s,18m/s2
(d) 9m/s,Om/s?
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Answer 1

Answer :

The displacement of a particle moving along x axis is given by x = 18t

We have to find velocity and acceleration of the particle$.$

Given that : x = 18t

In order to find velocity of the particle we have to differentiate the given displacement equation.

➝ v = dx/dt

➝ v = d(18t) / dt

➝ v = 18 m/s

Here we can see that, velocity of particle doesn't depend on time. It means body is moving at a constant velocity which is equal to 18m/s.

In order to find acceleration of the particle we have to again differentiate velocity equation.

➝ a = dv/dt

➝ a = d(18)/dt

➝ a = 0 m/s²

Body doesn't have acceleration.

∴ (B) is the correct answer!

Answer 2

$⛄ \fbox{ \: given}$

displacement= 18 t along X axis

time = 2 second

____________________________________

$⛄ \fbox{to \: find}$

1. velocity

1. velocity2. acceleration

_______________________________

$\fbox{solution}$

In order to find the velocity we have to differentiate x= 18t.

$d(v) = \frac{d(x)}{dt}$

$dv = \frac{18t}{dt} = 18 \frac{m}{second}$

♠️Velocity of the particle here is independent of time . This means the particle is moving with a constant velocity.

⛄To find acceleration we have to again differentiate the velocity now.

$d(a) = \frac{d(v)}{dt}$

⛄Differentiation of a constant is zero

$d(a) = \frac{18}{dt} = 0$

Therefore acceleration is 0.

$\fbox{therefore option B is correct.}$