How much time elapses from start to stop?

Question

An electric vehicle starts from rest and accelerates at a rate of 2.0 meter per seconds squared in a straight line until it reaches a speed of 20 meter per second. The vehicle then slows at a constant rate of 1.0 meters per second squared until it stops. How much time elapses form start to stop? How far does the vehicle travel from start to stop?

Answer 1

v=velocity
vo-initial velocity
a=accel
t=time

v=v0+at
20=0+2t => t=10

v=v0+at
1=20+(-1t)
-19=-t
t=19

total time = 19+10=29 seconds

Answer 2

T1 = 20/2 = 10 sec
T2 = 20/1 = 20 sec
Ttot = T1 + T2 = 30 sec

D1 = ½at² = ½*2*10² = 100 m
D2 = ½at² = ½*1*20² = 400 m
Dtot = D1+D2 = 500 m

Answer 3

Before the car slows down (i.e., it decelerates),
Initial velocity of the vehicle, u1=0 m/s [Since it was at rest before moving]
Final velocity of the vehicle = 20 m/s
Acceleration of the vehicle, a1=2 m/s^2
Let the time elapsed before the car slows down be t1 seconds.
Then, according to the 1st Equation of Motion,
v1 = u1 + a1*t1
so, 20 = 0 + 2*t1
i.e., t1 = 10 seconds

After this, the car slows down.
So, initial speed of the car AFTER slowing down = Final speed of the car BEFORE slowing down, u2 = 20 m/s
Final speed of the car after slowing down, v2 = 0 m/s [Since it stops, finally]
Acceleration of the car after slowing down, a2 = -1m/s^2 [Since the car is slowing down]
Let the time elapsed till the car comes to rest after slowing it down be t2 seconds.
Then, again according to the 1st Equation of Motion,
v2 = u2 + a2*t2
so, 0 = 20 + (-1)*t2
i.e., t2 = 20 seconds

Therefore, total time elapsed since the car started from rest until it stops = t1 + t2 = (10 + 20) seconds = 30 seconds.

Now, distance travelled by the car before slowing down
= u1*t1 + 1/2 * a1 * t1^2
= 0*t1 + 1/2 * 2 * 10^2
= 0 + 100
= 100 metres
Again, distance travelled by the car before stopping after it started slowing down = u2*t2 + 1/2*a2*t2^2
= 20*20 + 1/2*(-1)*20^2
= 400 - 200
= 200 metres
Therefore, total distance covered during the whole journey=(100+200) metres = 300 metres.