A car is brought to rest from 90 km/h in 20 seconds. What is its acceleration?

$$v_i = 90 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}}$$ $$v_i = \frac{90000}{3600} \text{ m/s}$$ $$v_i = 25 \text{ m/s}$$

The final velocity is $v_f = 0 \text{ m/s}$.

$$a = \frac{0 \text{ m/s} - 25 \text{ m/s}}{20 \text{ s}}$$ $$a = \frac{-25 \text{ m/s}}{20 \text{ s}}$$ $$a = -1.25 \text{ m/s}^2$$

The acceleration is $\boxed{-1.25 \text{ m/s}^2}$. The negative sign indicates deceleration.

6. A train starts from rest and attains a velocity of 180 km/h after 500 seconds. Calculate the acceleration.
Given:
Initial velocity, $v_i = 0 \text{ km/h}$ (starts from rest)
Final velocity, $v_f = 180 \text{ km/h}$
Time, $t = 500 \text{ s}$

$$v_i = 0 \text{ m/s}$$ $$v_f = 180 \text{ km/h} \times \frac{1000 \text{ m}}{1 \text{ km}} \times \frac{1 \text{ h}}{3600 \text{ s}}$$ $$v_f = \frac{180000}{3600} \text{ m/s}$$ $$v_f = 50 \text{ m/s}$$

$$a = \frac{50 \text{ m/s} - 0 \text{ m/s}}{500 \text{ s}}$$ $$a = \frac{50 \text{ m/s}}{500 \text{ s}}$$ $$a = 0.1 \text{ m/s}^2$$

The acceleration is $\boxed{0.1 \text{ m/s}^2}$.