Chapter 2, Problem 51QAP

To determine

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

Explanation of Solution

Given info:

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

Car is accelerating constantly at $3{\text{m/s}}^2$.

At time $t=6\text{s}$ the velocity of the car is $20\text{m/s}$.

Formula used:

Formula to find the distance travelled in term of velocity and time is,
  $d=v\times t\text{Equation-1}$

Another formula to find the distance travelled in term of speed and acceleration is,
  $d=ut+\frac{1}{2}a{t}^2\text{Equation-2}$

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

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

Find the position of car:

As car is starting from rest its initial velocity is zero. Finding the position of car using equation-2.
  $\begin{array}{l}{d}_{car}=\frac{1}{2}\times 3m{s}^{-2}{\left(ts\right)}^2\\ d_{car}=1.5t^{2}m\text{Equation-3}\end{array}$

By changing the value of time in equation-3 from $t=0$to $t=6\text{s}$draw a table showing the position of car at different time.

Time	$t=0$	$t=\text{1}\text{s}$	$t=\text{2}\text{s}$	$t=\text{3}\text{s}$	$t=\text{4}\text{s}$	$t=\text{5}\text{s}$	$t=\text{6}\text{s}$
Position of car (   $d_{car}$ )	$0\text{m}$	$1.5\text{m}$	$6\text{m}$	$13.5\text{m}$	$24\text{m}$	$37.5\text{m}$	$54\text{m}$

Find the position of truck using equation-1.

  $\begin{array}{c}{d}_{truck}=20\text{m/s}\times t\text{s}\\ =20t\text{m}\text{Equation-4}\end{array}$

By changing the value of time in equation-4 from $t=0$to $t=6\text{s}$draw a table showing the position of truck at different time.

Time	$t=0$	$t=\text{1}\text{s}$	$t=\text{2}\text{s}$	$t=\text{3}\text{s}$	$t=\text{4}\text{s}$	$t=\text{5}\text{s}$	$t=\text{6}\text{s}$
Position of car (   $d_{truck}$ )	$0\text{m}$	$20\text{m}$	$40\text{m}$	$60\text{m}$	$80\text{m}$	$100\text{m}$	$120\text{m}$

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.

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.