Dragsters can actually reach a top speed of 145 m/s in only...

Dragsters can actually reach a top speed of 145 m/s in only 4.45 s—considerably less time than given in Example 2.10 and Example 2.11. (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 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.

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Key Concepts

Average Acceleration

Average acceleration is defined as the change in velocity divided by the change in time. This concept is fundamental in kinematics for describing how quickly an object speeds up or slows down over a given period. It provides a simplified measure even if the actual acceleration varies over time.

Kinematic Equations

Kinematic equations relate displacement, velocity, acceleration, and time under the assumption of constant acceleration. These equations allow calculation of unknown variables when some are provided, such as using the equation v² = v?² + 2a s to find the final speed without directly knowing the time of travel.

Variable Acceleration and its Implications

In many real-world scenarios, such as drag racing, the acceleration is not constant. Instead, the acceleration may be greater at the start due to increased engine output and then decrease as various factors come into play. A variable acceleration profile can result in a greater final velocity over a fixed distance compared to what a constant average acceleration would predict, highlighting the limitations of simplified constant acceleration models.

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