Question

A car starts from rest moving along a line, first with acceleration a= $2m/s^2$ , then uniformly and finally decelerating at the same rate and comes to rest. The total time of motion is $10$ sec. The average speed during this time is $3.2m/s$. How long does the car move uniformly?(in seconds)

• A. $4$
  
• B. $5$
  
• C. $6$
  
• D. $7$
  

Answer 1

The correct option is C $6$

As average speed is given so distance or displacement of the body is given by $3.2\times 10=32m$

Distance covered while acceleration and retardation are the same. because time taking to 0 to v is equal to that of v to 0 as the value of acceleration and retardation is the same. Using $v^2-u^2=2as$

Break the journey in 3 parts acceleration, retardation, and uniform motion.

And let uniform motion is performed for t sec.

So $32=2[0.\frac{(10-t)}{2}+\frac{1}{2}.2(\frac{10-t}{2}{)}^2]+v.t$

Where $v=2.\left(\frac{10-t}{2}\right)$

Putting value of v in above equation we get $t=6sec$

So the body will move with uniform velocity for middle 2 sec and accelerated for first w sec and retarded for the last 2 sec.

So option C is the best possible answer.