Example 11
A particle moves along a straight line and passes through a fixed point with an initial velocity of 4 . Its acceleration, a ,t seconds after passing through O is given by a = 4 - 2t.
(a)calculate
(i) the instantaneous velocity, in me, of the particle when t = 7
(ii) the maximum velocity in ms–¹, of the particle.
(b) Find the possible values of t, in seconds, when the velocity of the particle is 7 ms–¹.,t seconds after passing through O is given
by a = 4 - 2t.
Solution
(a) (i) Given acceleration function,
So, velocity function,
When and ,
So,
Thus, at time,
When ,
Hence, the instantaneous velocity of the particle when is
(ii) Maximum velocity,
So,
Since , is maximum when .
Hence, maximum velocity of the particle
(b) When the instantaneous velocity of the particle is
or
Thus, the possible values of are 1 second and 3 seconds.