Question

If a car accelerates from a stationary starting position, what difference would it make to the velocity of the car to gradually increase the amount of acceleration to some maximum value, rather than maintain the acceleration at this maximum value from the beginning?

Answer 1

we know that the accelerating objects are constantly changing their velocity, one can say that the distance traveled/time is not a constant value in an accelerated motion.

In a motion with increasing acceleration the increase in velocity per unit time is not constant, so with every fixed time interval increase in velocity is not constant.

We can understant this with following table for fixed acceleration and changing acceleration:

Constant Acceleration, we see that difference of velocity is 4m/s for each succesive time interval.

time(s)	Velocity(m/s)
0	0
1	4
2	8
3	12

Increasing acceleration

time(s)	Velocity(m/s)
0	0
1	2
2	6
3	14