A race car accelerates on a straight track from 0 to 100 km/h in 6s. Another race car accelerates from 0 to 100 km/h in 5s. Compare the velocities and accelerations of the cars during their races.
To compare the velocities and accelerations of the two race cars, we first need to understand the definitions of velocity and acceleration.
Velocity is the rate at which an object changes its position. It is a vector quantity, which means it has both magnitude (speed) and direction.
Acceleration, on the other hand, is the rate at which an object changes its velocity. It is also a vector quantity.
In this case, both race cars start from rest (0 km/h) and accelerate to a speed of 100 km/h. The time it takes for each car to reach this speed is given: 6 seconds for the first car and 5 seconds for the second car.
To compare their velocities, we can calculate the average velocity for each car. Average velocity is defined as the total displacement (change in position) divided by the total time taken.
For the first car, its initial velocity is 0 km/h, and its final velocity is 100 km/h. The total displacement is 100 km/h - 0 km/h = 100 km/h. Divide this by the total time taken (6 seconds) to find the average velocity.
Average velocity of the first car = (100 km/h) / (6 s) = 16.67 km/h/s
For the second car, the initial velocity is also 0 km/h, the final velocity is 100 km/h, and the total time taken is 5 seconds. Using the same formula:
Average velocity of the second car = (100 km/h) / (5 s) = 20 km/h/s
Comparing the average velocities, we can see that the second car has a higher average velocity than the first car. This means that the second car covers a greater displacement in a shorter amount of time compared to the first car.
Now let's compare their accelerations. Acceleration is defined as the change in velocity divided by the time taken.
For the first car, the change in velocity is 100 km/h - 0 km/h = 100 km/h. Divide this by the time taken (6 seconds) to find the acceleration.
Acceleration of the first car = (100 km/h) / (6 s) = 16.67 km/h/s
For the second car, the change in velocity is again 100 km/h - 0 km/h = 100 km/h, and the time taken is 5 seconds. Applying the formula:
Acceleration of the second car = (100 km/h) / (5 s) = 20 km/h/s
Comparing the accelerations, we see that the second car has a higher acceleration than the first car. This means that the second car is able to change its velocity more rapidly than the first car.
In summary, during their races from 0 to 100 km/h, the second car has both a higher average velocity and a higher acceleration compared to the first car.