Answer:
1.8m/s
Step-by-step explanation:
Given:
speed;
v = 5t² - 2t + 2 ---------------(i)
(i) First, find the acceleration a by differentiating the speed equation in equation (i) with respect to t as follows;
a = [tex]\frac{dv}{dt}[/tex]
a = [tex]\frac{d}{dt} [5t^2 - 2t + 2][/tex]
a = 10t - 2 ---------------------(ii)
(ii) Next, find the moment (time) when the acceleration is zero. This is done by substituting a = 0 into equation(ii) as follows;
0 = 10t - 2
Solve for t
10t = 2
t = 2 / 10 = 0.2
Therefore, at t = 0.2s, the acceleration is zero.
(iii) Now, find the velocity at time t = 0.2s when the acceleration is zero. This is done by substituting the value of t = 0.2s into equation (i) as follows;
v = 5(0.2)² - 2(0.2) + 2
v = 0.2 - 0.4 + 2
v = 1.8
Therefore, the speed at the moment when acceleration is zero is 1.8m/s
NB: Since the units of measurement are not given, the S.I units are used. Hence m/s for speed.
