# Solving for Car Speed and Stopping Time in a Braking Scenario

• Alexanddros81
In summary, the conversation discusses the application of brakes on a car, resulting in a decrease in speed at a rate of 10 ft/s^2. The question asks for the initial speed of the car and the time it takes to come to a stop, with the solution using SUVAT formulas. The final answers appear to be correct.
Alexanddros81

## Homework Statement

11.9 The brakes of a car are applied, causing it to slow down at a rate of ##10 ft/s^2##.
Knowing that the car stops in 300 ft, determine (a) how fast the car was traveling immediately
before the brakes were applied, (b) the time required for the car to stop

## The Attempt at a Solution

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Can you check my solution?

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Acceleration is constant, so your integration leads to the standard SUVAT formulas, that you may be expected to know:

##v^2 - v_0^2 = 2as##

##v - v_0 = at##

Not that integrating is wrong, but it's unusual to see it in these cases.

Alexanddros81

## 1. What is the difference between speed and velocity?

Speed is a measure of how fast an object is moving, while velocity takes into account the direction of motion in addition to speed. In other words, velocity is a vector quantity while speed is a scalar quantity.

## 2. How is acceleration calculated in car motion?

Acceleration is the rate of change of velocity over time. In car motion, it can be calculated by dividing the change in velocity by the change in time. This can be represented by the equation a = (vf - vi)/t, where a is acceleration, vf is final velocity, vi is initial velocity, and t is time.

## 3. What is the difference between average and instantaneous acceleration?

Average acceleration is the overall change in velocity over a period of time, while instantaneous acceleration is the acceleration at a specific moment in time. In car motion, average acceleration can be calculated by dividing the change in velocity by the total time, while instantaneous acceleration can be found by taking the derivative of the car's velocity with respect to time.

## 4. How does displacement differ from distance in car motion?

Displacement is a measure of the change in position of an object, while distance is the total length traveled by the object. In car motion, displacement takes into account the direction of motion, while distance does not. Displacement can be calculated by subtracting the initial position from the final position.

## 5. What is the difference between uniform and non-uniform motion in cars?

Uniform motion is when the car travels at a constant speed, while non-uniform motion is when the speed of the car changes over time. In other words, the car's velocity is constant in uniform motion, while it varies in non-uniform motion. Uniform motion can be represented by a straight line on a position-time graph, while non-uniform motion will have a curved line.

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