Question Video: Finding the Uniform Acceleration of a Car in a Given Time given Its Initial and Final Velocities Mathematics

A car was moving in a straight line at 45 km/h. Given that the velocity decreased at a constant rate until the car came to rest 10 seconds after the driver hit the brakes, calculate the deceleration of the car.

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Video Transcript

A car was moving in a straight line at 45 kilometers per hour. Given that the velocity decreased at a constant rate until the car came to rest 10 seconds after the driver hit the brakes, calculate the deceleration of the car.

We can answer this question using the equations of constant acceleration, known as the SUVAT equations, where 𝑠 is the displacement of the car measured in meters, 𝑢 and 𝑣 are the initial and final velocities, respectively, measured in meters per second, 𝑎 is the acceleration measured in meters per second squared, and 𝑡 is the time measured in seconds.

In this question, we know that the initial velocity, the speed the car was moving with initially, is 45 kilometers per hour. The car came to rest after 10 seconds. Therefore, 𝑡 is equal to 10 seconds and the final velocity is zero kilometers per hour. Our first step is, therefore, to calculate the value of 𝑎 which will lead us to the deceleration of the car. We notice that the velocities are given in kilometers per hour and not in the SI base units of meters per second. There are 1,000 meters in one kilometer. There are also 3,600 seconds in one hour.

The initial velocity was 45 kilometers per hour. If we multiply the numerator by 1,000 and the denominator by 3,600, we will obtain the velocity in meters per second. The car travels 45,000 meters in 3,600 seconds. This simplifies to 12.5 meters in one second. The initial velocity of the car is, therefore, equal to 12.5 meters per second. As the car came to rest, the final velocity is zero meters per second.

We can now substitute these values into one of our equations of uniform acceleration to calculate 𝑎. We will use the equation 𝑣 is equal to 𝑢 plus 𝑎𝑡. Substituting in our values of 𝑣, 𝑢, and 𝑡, we have zero is equal to 12.5 plus 10𝑎. Subtracting 12.5 from both sides of this equation, negative 12.5 is equal to 10𝑎. We can then divide both sides of this equation by 10, giving us 𝑎 is equal to negative 1.25.

The acceleration of the car is, therefore, equal to negative 1.25 meters per second squared. As we need to calculate the deceleration, this will be the absolute value or magnitude of this. The deceleration of the car is, therefore, equal to 1.25 meters per second squared.

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