A car traveling at an initial velocity of $v=20m/s$ comes to a stop in $t=4s$ after the brakes are applied. What is the magnitude of the car's acceleration $a_x$ during this time?

• A. $5m/s^2$
• B. $80m/s^2$
• C. $0.2m/s^2$
• D. $16m/s^2$

Answer: (A)

Verified step by step guidance

1. Identify the known quantities: initial velocity \(v = 20\ \text{m/s}\), final velocity \(v_f = 0\ \text{m/s}\) (since the car comes to a stop), and time \(t = 4\ \text{s}\) over which the velocity changes.
2. Recall the formula for acceleration when velocity changes uniformly over time: \(a = \frac{v_f - v}{t}\).
3. Substitute the known values into the formula: \(a = \frac{0 - 20}{4}\).
4. Calculate the magnitude of the acceleration by taking the absolute value of the result, since acceleration is a vector and the problem asks for magnitude.
5. Interpret the result as the magnitude of the car's acceleration during the braking period.