Question:
a car starting from rest accelerates at the rate f through a distance s then continues at a constant speed for a time t and then decelerate at a rate f/2 to come to rest if the total distance travelled is 15 s then prove that s =ft²/72
Answer:
We can devide this question in 3 steps.
1. When car moving with acceleration f and covers the distance s.
Initial speed =0
Thus using the third equation of motion we can find the final velocity after moving a distance s.
v2=0+2fs
v=√2fs
2. After that the car moved at a constant speed for t time we can calculate the distance travelled.
Let the distance covered in this step is s2
s2= vt = √2fs*t
3. Now after that it is decelerated by f/2 so we can find the distance covered as-
Let the distance covered in this step is s3
Using third equation of motion
0=v2-2*f/2*s3
( here,Final velocity is zero and initial velocity is v)
So, s3 = 2s
Now total distance travelled is 15s
So,
15 s= s+√2fs*t + 2s
=12 s =√2fs*t
s=f t2/72
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