Question

A particle is moving along X axis . The position of the particle at any instant is given by X =5 + 6t square , where X is in meters , t in seconds . What is the velocity of the particle at t = 2s?

Answer 1

The velocity of the particle at t = 2s is given as :

• A particle is moving along X axis . • The position of the particle at any instant is given by X =5 + 6t square , where X is in meters , t in seconds.

• Velocity = dx / dt

= d ( 5 + 6t ) / dt

= d(5) / dt + d(6t) / dt

= 0 + 6 = 6 m/s

• It is clear that velocity is constant at any instant of time as it is independent of time

• Therefore, velocity at t = 2s is 6 m/s

Answer 2

Answer:

24 m/s   (along x-axis)

Explanation:

Velocity for any short period of time is rate of change of displacement when t tends to 0 (time taken is near to 0, or as small as possible). Therefore,

velocity = $\lim_{\delta t \rightarrow0} \frac{\delta x}{\delta t}$

velocity = $\frac{dx}{dt}$

In the given equation, x = 5 + 6t²

=> v = $\frac{d}{dt}(5 + 6t^2)$

=> v = $\frac{d}{dt}5$ + $\frac{d}{dt}(6t^2)$

=> v = 0 + 2*6t

=> v = 12t

Therefore, at t = 2,

=> v = 12(2) = 24 m/s