Question

A top-fuel dragster starts from rest and has a constant acceleration of $40.0 \mathrm{m} / \mathrm{s}^{2} .$ Concepts: (i) At time $t$ the dragster has a certain velocity. Keeping in mind that the dragster starts from rest, when the time doubles to $2 t,$ does the velocity also double? (ii) When the time doubles to $2 t$ does the displacement of the dragster also double? Calculations: What are the (a) final velocities and (b) displacements of the dragster at the end of $2.0 \mathrm{s}$ and at the end of twice this time, or $4.0 \mathrm{s} ?$

Name: Problem 91, Chapter 2: Physics
Uploaded: 2021-03-09T10:15:14-08:00
Duration: 2 min 16 s
Channel: Sachin Rao

   A top-fuel dragster starts from rest and has a constant acceleration of $40.0 \mathrm{m} / \mathrm{s}^{2} .$ Concepts: (i) At time $t$ the dragster has a certain velocity. Keeping in mind that the dragster starts from rest, when the time doubles to $2 t,$ does the velocity also double? (ii) When the time doubles to $2 t$ does the displacement of the dragster also double? Calculations: What are the (a) final velocities and (b) displacements of the dragster at the end of $2.0 \mathrm{s}$ and at the end of twice this time, or $4.0 \mathrm{s} ?$

Physics

John D. Cutnell,… 11th Edition

Chapter 2, Problem 91

Instant Answer

Solved by Expert Sachin Rao

03/09/2021

Step 1

Since the dragster starts from rest, the initial velocity $u$ is $0 \, \mathrm{m/s}$. The velocity $v$ at time $t$ can be found using the equation $v = u + at$, where $a$ is the acceleration and $t$ is the time. Substituting the given values, we get $v = 0 + 40t = Show more…

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A top-fuel dragster starts from rest and has a constant acceleration of $40.0 \mathrm{m} / \mathrm{s}^{2} .$ Concepts: (i) At time $t$ the dragster has a certain velocity. Keeping in mind that the dragster starts from rest, when the time doubles to $2 t,$ does the velocity also double? (ii) When the time doubles to $2 t$ does the displacement of the dragster also double? Calculations: What are the (a) final velocities and (b) displacements of the dragster at the end of $2.0 \mathrm{s}$ and at the end of twice this time, or $4.0 \mathrm{s} ?$

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Key Concepts

Constant Acceleration

This concept explains that when an object accelerates at a steady rate, its change in velocity over time is consistent. It serves as the foundation for using kinematic equations, particularly when the object starts from rest, which means its initial velocity is zero.

Velocity-Time Relationship

Under constant acceleration, velocity increases linearly over time, described by the equation v = at. This means that if time is doubled, the velocity also doubles, assuming the acceleration remains unchanged.

Displacement-Time Relationship

Displacement under constant acceleration follows the quadratic equation s = ½at². As a result, doubling the time does not just double the displacement but increases it by a factor of four because displacement depends on the square of the time elapsed.

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