Let's solve the given problem step by step.

Given dataLet's solve the given problem step by step.

Given

• Initial velocity $V_0 = 20 \, \text{m/s}$
• Time to stop $t = 20 \, \text{sec}$
• Final velocity $V = 0 \, \text{m/s}$ (since the car comes to a full stop)

(a) What is the car's acceleration?

To find the acceleration, we can use the first equation of motion: $V = V_0 + at$ Since the final velocity $V = 0$, the equation becomes: $0 = 20 + a \times 20$ Solving for acceleration $a$: $a = \frac{-20}{20} = -1 \, \text{m/s}^2$ So, the acceleration of the car is $-1 \, \text{m/s}^2$, which means it is decelerating at $1 \, \text{m/s}^2$.

(b) How far does it travel before stopping?

To find the distance travelled before stopping, we can use the second equation of motion: $s = V_0 t + \frac{1}{2} a t^2$ Substitute the known values: $s = 20 \times 20 + \frac{1}{2} \times (-1) \times (20)^2$ $s = 400 + \frac{1}{2} \times (-1) \times 400$ $s = 400 - 200 = 200 \, \text{m}$ So, the car travels 200 meters before coming to a stop.

Final Answers:

• (a) The car's acceleration is $-1 \, \text{m/s}^2$.
• (b) The car travels 200 meters before stopping.

Would you like further details or clarifications? Here are some related questions to deepen your understanding:

1. How would the results change if the time to stop was 10 seconds instead of 20 seconds?
2. What would happen to the distance travelled if the car was moving faster initially?
3. How would you calculate the stopping distance if the acceleration wasn't constant?
4. Can you determine the total time taken to stop if only the distance is known?
5. How would you graph the car’s velocity versus time during the stop?

Tip: When solving motion problems, always write down known values clearly to avoid confusion during calculations!