Chapter 3, Problem 64A

To determine

To Construct: A problem for which the given graph is part of the solution.

Explanation of Solution

Introduction:

The acceleration of an object is defined as the rate of change of velocity. The mathematical reorientation of acceleration is:

  $a=\frac{dv}{dt}$

Where, $a$ = acceleration

  $dv$ = change of velocity

  $dt$ = time interval

The meaning of positive acceleration is that the velocity of car is increasing with time. When the acceleration is negative, it means that the velocity of car decreases with time. At last when acceleration of object is zero, it means body is moving with constant velocity.

Suppose a car was initially moving with the acceleration of $5{\text{ m/s}}^2$ for $3\text{ s}$ . At $t=3\text{ s}$ , driver observed the rush on road and he suddenly reduces the acceleration of car to $1.5{\text{ m/s}}^2$ and then continued his journey for $t=8\text{ s}$ . At $t=8\text{ s}$ , the driver observed a red traffic light and then he applied break and his break produced a retardation of ${\text{2 m/s}}^2$ for next $t=2\text{ s}$ . Draw a acceleration-time graph which represents the motion of the car.