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The position of a particle moving in an xy plane is given by +[(6 m) – (7 m/s4)t4] . Calculate (a) when t = 2 s.

The position of a particle moving in an xy plane is given by   +[(6 m) – (7 m/s4)t4]  . Calculate (a) when t = 2 s.

Grade:11

1 Answers

Aditi Chauhan
askIITians Faculty 396 Points
9 years ago
Given:
Position of particle,236-1716_Capture.PNG
(a) The is the position of a particle, given as:
236-1705_2.PNG
(b) The velocity of the particle is given as:
236-328_3.PNG
Now we apply the property of differentiation given as:

236-196_4.PNG
Using the property of differentiation one can obtain the velocity vector as:
236-2192_5.PNG
(c) The acceleration vector\overrightarrow{a} of the particle is:
\overrightarrow{a} = \frac{\overrightarrow{v}}{dt}
Substitute the velocity vector in equation (1) to obtain the acceleration as:
236-618_7.PNG
At t = 2 s the acceleration vector is:

Therefore the acceleration vector of the particle at is .
236-2127_9.PNG
Therefore the acceleration vector of the particle at t = 2s is236-2037_10.PNG

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