Question

find the acceleration of the car in the two regions where the velocity was changing

Explanation:

To find the acceleration in each region, we use the formula for acceleration, \( a = \frac{\Delta v}{\Delta t} \), where \( \Delta v \) is the change in velocity and \( \Delta t \) is the change in time.

For Region \( a_1 \) (Green Region):

Step 1: Identify \( \Delta v \) and \( \Delta t \)

• Initial velocity (\( v_i \)): \( 0 \, \text{m/s} \) (at \( t = 5 \, \text{s} \))
• Final velocity (\( v_f \)): \( 30 \, \text{m/s} \) (at \( t = 10 \, \text{s} \))
• \( \Delta v = v_f - v_i = 30 - 0 = 30 \, \text{m/s} \)
• \( \Delta t = 10 - 5 = 5 \, \text{s} \)

Step 2: Calculate Acceleration

\( a_1 = \frac{\Delta v}{\Delta t} = \frac{30}{5} = 6 \)

For Region \( a_2 \) (Red Region):

Step 1: Identify \( \Delta v \) and \( \Delta t \)

• Initial velocity (\( v_i \)): \( 30 \, \text{m/s} \) (at \( t = 20 \, \text{s} \))
• Final velocity (\( v_f \)): \( 0 \, \text{m/s} \) (at \( t = 30 \, \text{s} \))
• \( \Delta v = v_f - v_i = 0 - 30 = -30 \, \text{m/s} \)
• \( \Delta t = 30 - 20 = 10 \, \text{s} \)

Step 2: Calculate Acceleration

\( a_2 = \frac{\Delta v}{\Delta t} = \frac{-30}{10} = -3 \)

Answer:

\( a_1 = 6 \)
\( a_2 = -3 \)