Velocity,average velicity,distance

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In summary, the automobile initially travels at a uniform speed of 55km/h and then accelerates at a rate of 5.4m/s squared to reach a new speed of 75km/h. To determine the time it takes to reach this new speed, the average velocity during the acceleration, and the distance traveled while accelerating, we can use the equations for uniformly accelerated motion. However, we must be careful with units when using these equations.
  • #1
john stewart
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An automobile is traveling uniformly at 55km/h. It then accelerates at 5.4m/s squared to 75km/h.

a. How long does it take to reach this new speed?
b. What is the average velocity as it speeds up?
c. How far does it travel while accelerating?
 
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  • #2
Do you know the equations that relate to uniformly accelerated motion? (Suvat equations)
You will need to take great care with units in this question.
 
  • #3
my book has many formulas for constant acceleration I don't know whick one to use
 
  • #4
john stewart said:
my book has many formulas for constant acceleration I don't know whick one to use


Well, think about it for a while. What quantities have you been given already? What is the unknown you're being asked to solve for? What equation will allow you to solve for that unknown quantity using those given quantities?
 
  • #5


a. To calculate the time it takes for the automobile to reach 75km/h, we can use the formula v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the given values, we get 75 = 55 + (5.4)t. Solving for t, we get t = 3.7 seconds. Therefore, it takes 3.7 seconds for the automobile to reach 75km/h.

b. The average velocity as the automobile speeds up can be calculated by taking the average of the initial and final velocities. In this case, the average velocity is (55 + 75)/2 = 65 km/h. This means that the automobile has an average velocity of 65 km/h while it is accelerating from 55 km/h to 75 km/h.

c. To calculate the distance traveled while accelerating, we can use the formula s = ut + (1/2)at^2, where s is the distance, u is the initial velocity, a is the acceleration, and t is the time. Plugging in the values, we get s = (55)(3.7) + (1/2)(5.4)(3.7)^2 = 203.05 meters. Therefore, the automobile travels 203.05 meters while accelerating from 55 km/h to 75 km/h.
 

1. What is velocity?

Velocity is a measure of an object's speed and direction. It is a vector quantity, meaning it has both magnitude (speed) and direction. In other words, it tells us how fast an object is moving and in what direction it is moving.

2. How is velocity different from average velocity?

Velocity and average velocity are two different ways of measuring an object's speed. Velocity is the instantaneous speed of an object at a specific moment, while average velocity is the total distance traveled divided by the total time taken. Average velocity takes into account any changes in speed or direction during the entire journey.

3. Can velocity be negative?

Yes, velocity can be negative. This indicates that the object is moving in the opposite direction of the positive direction chosen for the measurement. For example, if an object is traveling east and we choose east as the positive direction, then the object's velocity would be positive. However, if the object begins to travel west, its velocity would become negative.

4. How is distance related to velocity?

Distance and velocity are related in that velocity is the rate at which distance is covered. In other words, velocity is the change in distance over time. The greater the velocity, the more distance an object will cover in a given amount of time.

5. How can one calculate average velocity?

To calculate average velocity, you would divide the total distance traveled by the total time taken. For example, if a car travels 100 miles in 2 hours, the average velocity would be 50 miles per hour. This formula can also be written as velocity = distance/time.

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