Question

A car accelerates uniformly from rest to attain a speed of 20 m/s after covering a distance of 80 m. It then decelerates uniformly and comes to rest after covering further a distance of 160 m. The total time taken for this journey is....
Pls full solution

Answer 1

Case 1:  

Vi = 0 m/s ,   Vf = 20 m/s , S = 80 m

By using equation of motion, we get

2aS = Vf^2 - Vi^2

2a(80) = (20)^2 - 0^2

160 a = 400  ⇒ a = 400/160

a = 5/2

Also

Vf = Vi + at

20 = 0 + 5/2t

20 = 5/2t

2(20) = 5t

t = 40/5

t 1 = 8 sec

Case 2:  

Vi = 20 m/s ,   Vf = 0 m/s , S = 160 m

By using equation of motion, we get

2aS = Vf^2 - Vi^2

2a(160) = (0)^2 - (20)^2

320 a =  - 400  ⇒ a =  -400/320

a =  - 5/4

Also

Vf = Vi + at

0 =  20 + ( - 5/4 )t

- 20 = - 5/4 t

   20 = 5/4 t

4(20) = 5 t

t = 80/5

t 2 = 16 sec

Total time =  8 + 16 = 24 sec