The speedometer readings of a car are shown below. Find the acceleration of the car and its displacement.

Time

• 9:25 am: 36 km/h
• 9:45 am: 72 km/h

To find the acceleration and displacement of the car based on the speedometer readings, we can break down the problem into manageable steps. First, we need to convert the speed readings from kilometers per hour (km/h) to meters per second (m/s) since acceleration is typically expressed in meters per second squared (m/s²) and displacement in meters (m). Then, we can calculate the acceleration and displacement over the given time interval.

Step 1: Convert Speed to Meters per Second

The formula to convert km/h to m/s is:

Speed (m/s) = Speed (km/h) × (1000 m / 1 km) × (1 h / 3600 s)

Now, let's convert the speeds:

• At 9:25 am: 36 km/h = 36 × (1000 / 3600) = 10 m/s
• At 9:45 am: 72 km/h = 72 × (1000 / 3600) = 20 m/s

Step 2: Calculate the Acceleration

Acceleration is defined as the change in velocity over time. The formula for acceleration (a) is:

a = (final velocity - initial velocity) / time

Here, the initial velocity (u) is 10 m/s, and the final velocity (v) is 20 m/s. The time interval between 9:25 am and 9:45 am is 20 minutes, which we need to convert to seconds:

• 20 minutes = 20 × 60 = 1200 seconds

Now we can plug in the values:

a = (20 m/s - 10 m/s) / 1200 s = 10 m/s / 1200 s = 0.00833 m/s²

Step 3: Calculate the Displacement

Displacement can be calculated using the formula:

Displacement (s) = initial velocity × time + 0.5 × acceleration × time²

Using the initial velocity (u = 10 m/s), acceleration (a = 0.00833 m/s²), and time (t = 1200 s), we can find the displacement:

s = 10 m/s × 1200 s + 0.5 × 0.00833 m/s² × (1200 s)²

Calculating each part:

• First part: 10 m/s × 1200 s = 12000 m
• Second part: 0.5 × 0.00833 m/s² × 1440000 s² = 0.004165 × 1440000 = 6000 m

Now, adding both parts together:

s = 12000 m + 6000 m = 18000 m

Summary of Results

In summary, the acceleration of the car is approximately 0.00833 m/s², and the total displacement over the 20-minute interval is 18000 meters or 18 kilometers.