(1) A particle has an initial displacement of s= 30 metres when t = 0. The velocity of the particle is v= 6t² - 216t+1944 m/s (t > 0). (a) Find the displacement of the particle at time t. (b) Find the acceleration of the particle at time t. (c) What is the acceleration and displacement when v = 0?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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(1) A particle has an initial displacement of s = 30 metres when t = 0. The velocity
of the particle is v= 6t² - 216t+ 1944 m/s (t > 0).
(a) Find the displacement of the particle at time t.
(b) Find the acceleration of the particle at time t.
(c) What is the acceleration and displacement when v = 0?
Transcribed Image Text:(1) A particle has an initial displacement of s = 30 metres when t = 0. The velocity of the particle is v= 6t² - 216t+ 1944 m/s (t > 0). (a) Find the displacement of the particle at time t. (b) Find the acceleration of the particle at time t. (c) What is the acceleration and displacement when v = 0?
Expert Solution
Step 1

We know that the velocity is defined as the rate of change of the position of the object with respect

to the time.

Similarily, the acceleration is defined as the rate of change of the velocity of the object with respect

to the time.

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