Dragsters can actually reach a top speed of 145.0 m / s in only 4.45 s. (a) Calculate the averag

step 1 Question number 65 the top speed is given as 145 meter per second. The time is 4 .45 seconds. No

Dragsters can actually reach a top speed of 145.0 m / s in...

Dragsters can actually reach a top speed of $145.0 \mathrm{m} / \mathrm{s}$ in only $4.45 \mathrm{s}$. (a) Calculate the average acceleration for such a dragster. (b) Find the final velocity of this dragster starting from rest and accelerating at the rate found in (a) for $402.0 \mathrm{m}$ (a quarter mile) without using any information on time. (c) Why is the final velocity greater than that used to find the average acceleration? (Hint: Consider whether the assumption of constant acceleration is valid for a dragster. If not, discuss whether the acceleration would be greater at the beginning or end of the run and what effect that would have on the final velocity.)

Key Concepts

Average Acceleration

Average acceleration is the ratio of the total change in velocity to the time over which the change occurs. This concept provides a simplified view of motion, allowing one to determine a single acceleration value that characterizes how quickly the speed of an object increases or decreases over a time interval.

Kinematic Equations Under Constant Acceleration

Kinematic equations under constant acceleration are fundamental relationships that link displacement, velocity, acceleration, and time. They are derived under the assumption that acceleration remains constant throughout the motion, which simplifies calculations and predictions of motion parameters in idealized scenarios.

Variable Acceleration and Its Implications

In many practical situations, such as high-performance drag racing, acceleration is not constant. Variable acceleration means that the acceleration rate may be higher initially (when the vehicle is in traction) and could change over the course of the motion. This can result in outcomes, such as a final velocity after a given displacement, that differ from predictions made assuming constant acceleration.

Application of Kinematic Models to Real-World Dynamics

When applying kinematic models to situations like drag racing, it is crucial to evaluate the assumptions behind these models. Understanding that real-world factors can lead to non-uniform acceleration helps in interpreting results accurately, explaining why models based on constant acceleration might underestimate or overestimate certain motion parameters.

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