High School

A car accelerates from 11.2 m/s to 24.3 m/s while passing a truck, covering a distance of 38.1 m. Determine the acceleration that the car experiences.

Express your answer to two decimal places.

Answer :

The car experiences an acceleration of approximately 6.12 m/s² while passing the truck.

To determine the acceleration experienced by the car, we can use the formula:

acceleration = (final velocity - initial velocity) / time

In this case, the initial velocity (u) of the car is 11.2 m/s, the final velocity (v) is 24.3 m/s, and the distance covered (s) is 38.1 m.

First, let's find the time it took for the car to cover this distance. We can use the formula:

distance = (initial velocity + final velocity) * time / 2

Rearranging the formula to solve for time:

time = (2 * distance) / (initial velocity + final velocity)

Plugging in the given values:

time = (2 * 38.1) / (11.2 + 24.3)

Calculating the time:

time = 76.2 / 35.5
time ≈ 2.15 seconds (rounded to 2 decimal places)

Now, we can calculate the acceleration:

acceleration = (final velocity - initial velocity) / time

Plugging in the values:

acceleration = (24.3 - 11.2) / 2.15

Calculating the acceleration:

acceleration ≈ 6.12 m/s² (rounded to 2 decimal places)

Therefore, the car experiences an acceleration of approximately 6.12 m/s² while passing the truck.

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