To find the car's acceleration, we can use the kinematic equation for acceleration when initial velocity, final velocity, and time are given:

$a = \frac{v_f - v_i}{t}$

where:

• $v_f = 20.0 \, \text{m/s}$ (final speed of the car),
• $v_i = 0 \, \text{m/s}$ (initial speed, since the car starts at rest),
• $t = 5.0 \, \text{s}$ (time).

Substitute the values:

$a = \frac{20.0 \, \text{m/s} - 0 \, \text{m/s}}{5.0 \, \text{s}} = \frac{20.0 \, \text{m/s}}{5.0 \, \text{s}} = 4.0 \, \text{m/s}^2$

Answer:

The car's acceleration is $4.0 \, \text{m/s}^2$ in the positive $x$-direction.

Would you like further details on the steps?

Here are five related questions:

1. How would the acceleration change if the final speed was 30 m/s instead?
2. What distance would the car travel during this 5-second acceleration period?
3. If the car continued at the final speed of 20 m/s for another 10 seconds, what would be its total displacement?
4. What would the initial velocity need to be for the car to reach 20 m/s in only 3 seconds?
5. How much force would be required to produce this acceleration if the car’s mass is 1,000 kg?

Tip: Remember that constant acceleration problems often involve other kinematic equations, which can provide additional details like displacement and average velocity.