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# Estimating Forces in Deceleration

### Estimating Forces in Deceleration

We will learn to estimate the forces applied to result in deceleration of a car.

Will a car travelling at a high speed, requires more or less **braking force** to stop in the same stopping distance as a car travelling at a lower speed?

Complete this sentence: A larger braking force means a larger _________

If a vehicle accelerates at $25\space m/s{^2}$, it will speed up in the direction of motion. If it accelerates at $-25\space m/s{^2}$, how would you describe the motion of the vehicle?

We can **estimate** deceleration and the forces involved by using **typical** **values** and the formula for acceleration. We use the symbol $\sim$ to denote that a value is **approximate**.

We want to estimate the deceleration of a vehicle, using the formula ${v^2} - {u^2} = 2as$

If ${v^2} - {u^2}$ gives us the change in velocity, and $u$ is the initial velocity, what is $v$?

To find a change of velocity, use ${v^2} - {u^2}$.

This means you should subtract the square of the initial velocity, from the square of the final velocity.

If a vehicle is travelling at at typical speed of $\sim 13\space m/s$, and decelerates to a stop, what is the change in velocity?

If ${v^2} - {u^2} = 2as$, where $a$ is acceleration and $s$ is distance, how would you rearrange the formula to find the acceleration of a vehicle?

A) $a = {v^2}-{u^2}\times 2s$ B) $a={{v^2}-{u^2}\over 2s}$

Answer A or B.

Use the formula $a={{v^2}-{u^2}\over 2s}$ to find the acceleration involved if a vehicle is travelling at at typical speed of $\sim 13\space m/s$, and decelerates to a stop in 34 metres. Give your answer to 1 decimal place, and with the correct units used for acceleration.

The acceleration of the vehicle is negative, meaning it is accelerating in the opposite direction to its motion.

If you are describing the **deceleration** of the vehicle, you simply remove the negative sign. Therefore, the vehicle is **decelerating** at a rate of $2.5\space m/s$

A car comes to an emergency stop in 60 metres when travelling on a motorway. A **typical** motorway speed is $27\space m/s$ . Estimate the deceleration of the vehicle.

A car driver travelling at a typical speed of $\sim 12\space m/s$ spots a hazard approximately 40 metres ahead. What magnitude of **deceleration** does he need in order to stop the car in time to prevent a collision?

A car is in motion on a road with a 40 mile per hour speed limit. A **typical** speed on this road is$18\space m/s$ . He applies his brakes and stops within **approximately** 40 metres. Estimate his deceleration and give your answer as a whole number with the correct unit for deceleration.

Using the deceleration you have estimated from typical speeds and braking distance, you can then estimate the braking force involved, using **Newton's second law**. What is Newton's second law?

A car driver applies his brakes and decelerates at a rate of $5\space m/s{^2}$ . If a **typical** car has a mass of $\sim 1000\space kg$, estimate the braking force applied.

A car with a **typical** mass of $\sim 1000\space kg$ is travelling at a **typical** motorway speed of $\sim 27\space m/s$ . He decelerates to a stop in 50 metres in an emergency. Estimate the braking force applied.

Before you can find the force, you need to estimate the deceleration using the typical speed. What is the car's rate of deceleration? You can use the formula $a={{v^2}-{u^2}\over 2s}$. Give your answer in a whole number, with the correct unit for deceleration.

Now that you have estimated the deceleration, you can find the braking force using Newton's second law.

A small car with a mass of $\sim 700\space kg$ is travelling at **typical** speed of $\sim 12\space m/s$. Another car is blocking the road, approximately 30 metres in the distance. Estimate the deceleration and braking force needed to bring the car to a complete stop within this distance.

What deceleration is needed? Give your answer to 1 decimal place, and with correct units.

What magnitude of braking force is needed to cause this deceleration?