A toy car with charge q moves on a friction less horizontal plane surface under the influence of a uniform electric field

A toy car with charge q moves on a friction less horizontal plane surface under the influence of a uniform electric field $ \vec{E}$ . Due to the force $\vec{q E}$ , its velocity increases from 0 to 6 m/s in one second duration . At that instant the direction of field is reversed . The car continue to move for two more seconds under the influence of this field . The average velocity and average speed of the toy car between 0 to 3 seconds are respectively .

(a) 1 m/s , 3.5 m/s

(b) 1.5 m/s , 3 m/s

(c) 1 m/s , 3 m/s

(d) 2 m/s , 4 m/s

Sol: velocity increases from 0 to 6 m/s in one second

Acceleration , $ \displaystyle a = \frac{6-0}{1} = 6 m/s^2 $

$\displaystyle S_1 = \frac{1}{2}a (1)^2 $

$ \displaystyle S_1 = \frac{1}{2}\times 6 \times (1)^2 = 3 m$

Now , the direction of field is reversed , hence motion being retarded & momentarily comes to rest after next one second , after that direction is reversed .

$\displaystyle S_2 = 6 \times 1 – \frac{1}{2}\times 6 \times (1)^2 $

$ \displaystyle S_2 = 3 m $

$\displaystyle S_3 = \frac{1}{2}a (1)^2 = 3 m$

Average speed$\displaystyle = \frac{Total \;Distance}{Total \; time} $

$\displaystyle = \frac{9}{3} = 3 m/s$

Average velocity $\displaystyle = \frac{Displacement}{time} $

$ \displaystyle = \frac{3}{3} = 1 m/s$