Motion with Uniform Acceleration - Challenging Question 2

Challenging Question 2:
Zulkifli starts driving his car from home with a constant acceleration and reaches a velocity of 30 m/s in 6.0 seconds. Find

1. the acceleration of Zulkifli's car.
2. the displacement of Zulkifli's car 5.0 seconds after it started moving.
3. the displacement of Zulkifli's car in the fifth second..
4. velocity of Zulkifli's car at time t = 4.0 seconds?
5. velocity of Zulkifli's car after moving 30.0 meters from the starting point.

Answer:
It's advisable to list down all the information that we have.

Initial velocity, u = 0 (Start driving from his home)
Final velocity, v = 30 ms^-1
Time taken, t = 6s

a. Acceleration, a = ?
$$\begin{array}{l}\left(30\right)=(0)+a(6)\\ 6a=30\\ a=\frac{30}{6}=5m{s}^{-2}\end{array}$$
b. t = 5s, s = ?
$$\begin{array}{l}s=ut+\frac{1}{2}a{t}^2\\ s=(0)(5)+\frac{1}{2}(5){(}^5\\ s=62.5m\end{array}$$
(Note: We can't use v=30 for this calculation because it is the final velocity at 6s, but not 5s)

c. Fifth second is a period from 4s to 5s.

Displacement after 4s,
$$\begin{array}{l}s=ut+\frac{1}{2}a{t}^2\\ s=(0)(4)+\frac{1}{2}(5){(}^4\\ s=40m\end{array}$$
Displacement in the fifth second
= 62.5m - 40m = 22.5m

d. t = 4s, v = ?
$$\begin{array}{l}v=u+at\\ v=(0)+(5)(4)=20m{s}^{-2}\end{array}$$
e. s = 30.0m, v = ? $$\begin{array}{l}{v}^2=u^2+2as\\ v^2={(}^0+2(5)(30)\\ v^2=300\\ v=\sqrt{300}=17.3m{s}^{-1}\end{array}$$

Reference

$$\begin{array}{l}v=u+at\\ s=ut+\frac{1}{2}a{t}^2\\ v^2=u^2+2as\\ s=\frac{1}{2}(u+v)t\end{array}$$