Question

Please help me with questions 1, 2 and 3.
i need a step by step explanation

Answer 1

1) d

2) 5 m/s

3) 100

Step-by-step explanation:

The equation of position x for a constant acceleration a and an initial velocity v₀, initial position x₀, time t is:

(i)
`x=(1)/(2)at^2+v_0t+x_0`

The equation for velocity v and a constant acceleration a is:

(ii)
`v=at+v_0`

1) Solve equation (ii) for acceleration a and plug the result in equation (i)

(iii)
`a = (v -v_0)/(t)`

(iv)
`x = (v-v_0)/(2t)t^2+v_0t + x_0`

Simplify equation (iv) and use the given values v = 0, x₀ = 0:

(v)
`x=-(v_0)/(2)t + v_0t= (v_0)/(2)t`

2) Given v₀= 3m/s, a=0.2m/s², t=10 s. Using equation (ii) to get the final velocity v:
`v=at+v_0=0.2(m)/(s^2) * 10s+3(m)/(s)=2(m)/(s)+3(m)/(s)=5(m)/(s)`

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):

`f=(x(t_1))/(x(t_2))=((1)/(2)at_1^2 )/((1)/(2)at_2^2)=(t_1^2)/(t_2^2)=(10^2)/(1^2)=(100)/(1)`