A car slows down from $65\mathrm{km}/s$ to $30\mathrm{km}/s$ in $5s$. What is its acceleration?

• A. $\frac{30+65}{5}=\frac{95}{5}=19\mathrm{km}/s^2$
• B. $\frac{65-30}{5}=\frac{35}{5}=7\mathrm{km}/s^2$
• C. $\frac{30-65}{5}=\frac{-35}{5}=-7\mathrm{km}/s^2$
• D. $\frac{65+30}{5}=\frac{95}{5}=19\mathrm{km}/s^2$

Answer: (C)

Verified step by step guidance

1. Identify the initial velocity \(v_i = 65\ \text{km/s}\), the final velocity \(v_f = 30\ \text{km/s}\), and the time interval \(\Delta t = 5\ \text{s}\) over which the change occurs.
2. Recall that acceleration \(a\) is defined as the change in velocity divided by the time taken for that change, expressed as \(a = \frac{v_f - v_i}{\Delta t}\).
3. Substitute the known values into the acceleration formula: \(a = \frac{30 - 65}{5}\).
4. Calculate the numerator to find the change in velocity: \$30 - 65 = -35$ (the negative sign indicates the car is slowing down).
5. Divide the change in velocity by the time interval to find acceleration: \(a = \frac{-35}{5}\), which gives the acceleration in \(\text{km/s}^2\).