Example 12
A particle moves along a straight line and pusses through a fixed point O with a velocity of . The acceleration, a , at t seconds after passing through O is given by
(a) Determine the instantaneous displacement, in me, of the particle from O
(i) when (ii) when the particle is at rest
(b) Next, find distance, in m, travelled by the particle in the 7th second
Solution
Velocity function, v is given by
When and , then
Hence, at time t,
Displacement function, a is given by,
When and , then,
Hence, at time t,
(a) (i) When,
Hence, the instantaneous displacement when is 45 m.
(ii) When the particle is at rest, .
Then, Since ,
When ,
Hence, the instantaneous displacement when the particle is at rest is 72 m.
(b) When
From the number the distance travelled by the particle in the 7th second