Questions: A runner decreases his velocity from 20 m/s to 10 m/s in 2.0 s. What was his average acceleration? a 3.2 m/s^2 b -5.0 m/s^2 c 6.3 m/s^2 d 8.0 m/s^2

Transcript text: A runner decreases his velocity from $20 \mathrm{~m} / \mathrm{s}$ to $10 \mathrm{~m} / \mathrm{s}$ in 2.0 s . What was his average acceleration? a $\quad 3.2 \mathrm{~m} / \mathrm{s}^{2}$ b $\quad-5.0 \mathrm{~m} / \mathrm{s}^{2}$ c $6.3 \mathrm{~m} / \mathrm{s}^{2}$ d $8.0 \mathrm{~m} / \mathrm{s}^{2}$

Solution

Solution Steps

Step 1: Identify Initial and Final Velocities

Initial velocity ($v_i$) = $20 \, \text{m/s}$
Final velocity ($v_f$) = $10 \, \text{m/s}$

Step 2: Determine the Time Interval

Time interval ($t$) = $2.0 \, \text{s}$

Step 3: Use the Formula for Average Acceleration

The formula for average acceleration ($a$) is given by: \[ a = \frac{v_f - v_i}{t} \]

Step 4: Substitute the Values into the Formula

Substitute $v_f = 10 \, \text{m/s}$, $v_i = 20 \, \text{m/s}$, and $t = 2.0 \, \text{s}$ into the formula: \[ a = \frac{10 \, \text{m/s} - 20 \, \text{m/s}}{2.0 \, \text{s}} \]

Step 5: Calculate the Average Acceleration