Question

A car starting from rest is accelerated at constant rate until it attains a constant speed, $v$. It is then retarded at a constant rate until it comes to rest. Considering that the car moves with constant speed for half of the time of total journey, the average speed of the car for the journey is

• A. $\frac{v}{4}$
• B. $\frac{3v}{4}$
• C. $\frac{3v}{2}$
• D. Data insufficient

Answer 1

Answer: (B)

$\frac{3v}{4}$

$V_{avg}=\frac{distance}{time}$

Let the total time be $t$.

Average speed for 1st interval of $\frac{t}{4}$ is $\frac{v}{2}$

For 1st interval, $s_1=\frac{v}{2}\times \frac{t}{2}$

Average speed for $3rd$ interval of $\frac{t}{4}$ is $\frac{v}{2}$

For $3rd$ interval, $s_3=\frac{v}{2}\times \frac{t}{2}$

For $2nd$ interval, $s_2=v\times \frac{t}{2}$

Total distance $d=s_1+s_2+s_3$

Total time is $t$

$v_{avg}=\frac{d}{t}=\frac{3v}{4}$