Chapter 3, Problem 62A

To determine

Rank of acceleration of cars from greatest to least.

Answer to Problem 62A

Rank of acceleration of cars is,

  $\text{Car B}>\text{Car A}=\text{Car C}$

Explanation of Solution

Given :

Speed of car A changes from 0 m/sec to 17.9 m/sec in 4 sec.

Speed of car B changes from 0 m/sec to 22.4 m/sec in 3.5 sec.

Speed of car C changes from 0 m/sec to 26.8 m/sec in 6 sec.

Formula used:

Acceleration is the rate of change of velocity with respect to time and is given by,

  $a=\frac{v-u}{t}$

Where,

a is acceleration

u is initial velocity

v is final velocity

t is time taken to reach from initial to final velocity.

Calculation:

For car A,

Initial velocity is $u=0\text{ m/sec}$

Final velocity is $v=17.9\text{ m/sec}$

Time taken $t=4\text{ sec}$

Therefore , acceleration of car A is,

  $\begin{array}{c}a=\frac{17.9-0}{4}\\ \approx 4.47{\text{ m/sec}}^2\end{array}$

For car B,

Initial velocity is $u=0\text{ m/sec}$

Final velocity is $v=22.4\text{ m/sec}$

Time taken $t=3.5\text{ sec}$

Therefore , acceleration of car B is,

  $\begin{array}{c}a=\frac{22.4-0}{3.5}\\ =6.4{\text{ m/sec}}^2\end{array}$

For car C,

Initial velocity is $u=0\text{ m/sec}$

Final velocity is $v=26.8\text{ m/sec}$

Time taken $t=6\text{ sec}$

Therefore , acceleration of car C is,

  $\begin{array}{c}a=\frac{26.8-0}{6}\\ \approx 4.47{\text{ m/sec}}^2\end{array}$

It is observed that the acceleration of car B is greatest amongst all while the acceleration of car A and car C is almost same.

Conclusion:

Therefore, rank of acceleration of cars are

  $\text{Car B}>\text{Car A}=\text{Car C}$