Dynamics & Statics: Find Time for 5km Car Trip

In summary, the problem involves a car starting from rest and accelerating uniformly at 1m/second square to reach a maximum speed of 60kmph. It then travels at this speed for a certain amount of time before decelerating at a uniform rate of 0.5 m/second square until it comes to a complete stop. With a total distance of 5km, the problem asks for the total time taken for the car to cover this distance. To solve, the problem can be divided into three parts: acceleration, constant speed, and deceleration. Using equations vf= v(initial) + at and x= vi + .5at^2, the time for the first and third parts can be calculated. The
  • #1
herbgriffin
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Homework Statement


A car starts from rest and accelerates uniformly at the rate of 1m/second square to reach a maximum speed of 60kmph. It then travels at this speed for some time and finally decelerates at a uniform rate of 0.5 m/second square to come to rest. If the total distance traveled is 5km, determine the total time taken for the car to cover this distance.

Homework Equations





The Attempt at a Solution


 
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  • #2
First break this into three parts of acceleration, constant speed, and decceleration. Change the 60km/hr into meters per second to get uniform units. Knowing the final velocity, the acceleration and the initial velocity of zero, use vf= v(initial) + at to find the time for the first part. Do the same with the third part of the trip, but use a=-.5, vf=0 and vi=whatever 60km/hr is. Now for both parts use the equation x= vi + .5at^2 with x being distance. Plug in the respective values for each equation to find the distance of the third and first parts of the trip. Now subtract these from the total distance of 5 km and use the constant velocity of whatever 60km/hr in meters per second is to get time. Finally add all the times together.
 

1. How can I calculate the time for a 5km car trip?

To calculate the time for a 5km car trip, you will need to know the average speed of your car. Time can be calculated by dividing the distance (5km) by the speed in kilometers per hour (km/h). For example, if your car travels at an average speed of 60 km/h, the time for a 5km trip would be 5/60 = 0.0833 hours, or 5 minutes.

2. What is the difference between dynamics and statics?

Dynamics and statics are two branches of mechanics that deal with the study of motion and forces. Dynamics involves the study of objects in motion and the forces that cause that motion, while statics is concerned with objects at rest and the forces acting on them. In the context of a 5km car trip, dynamics would involve calculating the acceleration and velocity of the car, while statics would involve determining the forces acting on the car to keep it at a constant speed.

3. Can the terrain affect the time it takes for a 5km car trip?

Yes, the terrain can affect the time it takes for a 5km car trip. If the terrain is hilly or rough, it can slow down the car and increase the travel time. On the other hand, if the terrain is flat and smooth, the car can travel at a faster speed and decrease the travel time.

4. How does the weight of the car impact the time for a 5km trip?

The weight of the car can impact the time for a 5km trip because it affects the car's acceleration and speed. A heavier car will require more force to accelerate and maintain a certain speed, which can increase the travel time. On the other hand, a lighter car will require less force and can travel at a faster speed, potentially decreasing the travel time.

5. Are there any other factors that can affect the time for a 5km car trip?

Yes, there are several other factors that can affect the time for a 5km car trip. These include traffic conditions, weather, and the condition of the car (e.g. tire pressure, engine performance). These factors can impact the speed at which the car can travel and can either increase or decrease the travel time.

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