COLLEGE PHYSICS
COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 2, Problem 51QAP
To determine

The position time graph for the car and truck for time t=0to t=6s on the same set of axes.

Expert Solution & Answer
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Explanation of Solution

Given info:

Car is at rest at time t=0 and position x=0.

Car is accelerating constantly at 3m/s2.

At time t=6s the velocity of the car is 20m/s.

Formula used:

Formula to find the distance travelled in term of velocity and time is,
  d=v×t Equation-1

Another formula to find the distance travelled in term of speed and acceleration is,
  d=ut+12at2 Equation-2

Here, u is the initial velocity, v is the velocity at any time t and ais the acceleration.

To draw a position versus time graph we have to draw a table showing position of car from time t=0to t=6s.

Find the position of car:

As car is starting from rest its initial velocity is zero. Finding the position of car using equation-2.
  dcar=12×3ms2(ts)2dcar=1.5t2m Equation-3

By changing the value of time in equation-3 from t=0to t=6sdraw a table showing the position of car at different time.

    Time

      t=0

      t=1s

      t=2s

      t=3s

      t=4s

      t=5s

      t=6s
    Position of car
    (
      dcar
    )

      0m

      1.5m

      6m

      13.5m

      24m

      37.5m

      54m

Find the position of truck using equation-1.

  dtruck=20m/s×ts=20tm Equation-4

By changing the value of time in equation-4 from t=0to t=6sdraw a table showing the position of truck at different time.

    Time

      t=0

      t=1s

      t=2s

      t=3s

      t=4s

      t=5s

      t=6s
    Position of car
    (
      dtruck
    )

      0m

      20m

      40m

      60m

      80m

      100m

      120m

We draw position time graph by taking value of time on x-axis and position on y-axis.

The shape of position time graph for car is curve and for truck is a straight line.

Graph shows car is accreting from rest and truck is moving with constant velocity.

COLLEGE PHYSICS, Chapter 2, Problem 51QAP
Conclusion:

Thus,the shape of position time graph for car is curve and for truck is straight line.

Graph shows car is accreting from rest and truck is moving with constant velocity.

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Chapter 2 Solutions

COLLEGE PHYSICS

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Position/Velocity/Acceleration Part 1: Definitions; Author: Professor Dave explains;https://www.youtube.com/watch?v=4dCrkp8qgLU;License: Standard YouTube License, CC-BY