Finding Acceleration: Motorist Travels 0.2km in 45-99km/h

In summary, a motorist enters a freeway at 45km/h and accelerates uniformly to 99 km/h, traveling 0.2km according to the car's odometer. To find the acceleration, the formula v2 = u2 + 2as is used, resulting in a value of 5400 m/sec2 after converting the units correctly.
  • #1
adoado
72
0

Homework Statement



A motorist enters a freeway at 45km/h and accelerates uniformly to 99 km/h. From the odometer of the car, the driver knows she has traveled 0.2km. Find the acceleration of the car.

Homework Equations





The Attempt at a Solution



I attempted this:

v2 = u2 + 2as

Substituting the values in I got this:
(992 -452)/0.4 = a

this gives 19440, so converting to m/sec I think I get 5400 m/sec2

This is definitely not right, any ideas why?

Cheers,
Adrian :)
 
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  • #2
adoado said:
this gives 19440, so converting to m/sec I think I get 5400 m/sec2
What units do you think the 19440 would be in? Check your conversion.

The best thing to do is change units to m/s and m before you use them in the formula.
 
  • #3
Got it! Thanks a bunch!

Cheers,
Adrian
 

1. How is acceleration calculated in this scenario?

Acceleration is calculated by dividing the change in velocity (final velocity - initial velocity) by the time it took for the change to occur. In this case, the final velocity is 99km/h and the initial velocity is 45km/h, and the change occurred over a distance of 0.2km. So the acceleration would be (99km/h - 45km/h) / (0.2km) = 270km/h/s.

2. Why is it important to know the acceleration of a motorist?

Knowing the acceleration of a motorist can help us understand how quickly their speed is changing and how long it takes for them to reach a certain speed. This information is crucial for ensuring safe driving and for designing roads and vehicles that can handle different acceleration rates.

3. How does acceleration affect a vehicle's fuel consumption?

Higher acceleration rates require more fuel to be burned in order to achieve the desired speed. This is because acceleration is directly related to the force required to move the vehicle, which is powered by the engine. A more gradual acceleration can help improve fuel efficiency.

4. Is there a limit to how much a motorist can accelerate?

Yes, there are physical limits to acceleration. The maximum acceleration a vehicle can achieve is determined by its engine power, weight, and traction. In addition, human drivers also have limits to how quickly they can react and control the vehicle, which can impact the acceleration rate.

5. How can acceleration be measured in real-world scenarios?

Acceleration can be measured using specialized equipment such as accelerometers or by analyzing changes in speed and time data. In this scenario, the acceleration can be measured by recording the time it took for the motorist to travel 0.2km and their change in velocity. Speedometers in vehicles can also provide real-time acceleration data.

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