Answer:
1) d
2) 5 m/s
3) 100
Explanation:
The equation of position x for a constant acceleration a and an initial velocity v₀, initial position x₀, time t is:
(i) [tex]x=\frac{1}{2}at^2+v_0t+x_0[/tex]
The equation for velocity v and a constant acceleration a is:
(ii) [tex]v=at+v_0[/tex]
1) Solve equation (ii) for acceleration a and plug the result in equation (i)
(iii) [tex]a = \frac{v -v_0}{t}[/tex]
(iv) [tex]x = \frac{v-v_0}{2t}t^2+v_0t + x_0[/tex]
Simplify equation (iv) and use the given values v = 0, x₀ = 0:
(v) [tex]x=-\frac{v_0}{2}t + v_0t= \frac{v_0}{2}t[/tex]
2) Given v₀= 3m/s, a=0.2m/s², t=10 s. Using equation (ii) to get the final velocity v:[tex]v=at+v_0=0.2\frac{m}{s^2} * 10s+3\frac{m}{s}=2\frac{m}{s}+3\frac{m}{s}=5\frac{m}{s}[/tex]
3) Given v₀=0m/s, t₁=10s, t₂=1s and x₀=0. Looking for factor f = x(t₁)/x(t₂) using equation(i) to calculate x(t₁) and x(t₂):
[tex]f=\frac{x(t_1)}{x(t_2)}=\frac{\frac{1}{2}at_1^2 }{\frac{1}{2}at_2^2}=\frac{t_1^2}{t_2^2}=\frac{10^2}{1^2}=\frac{100}{1}[/tex]
