A bus travel 400 m between 2 stops. It starts from rest and accelerates at 1.5 m / s ^ 2 until it reaches a speed of 5m / s. The bus continuous at this speed and then decelerates at 2 m / s ^ 2 until it comes to a stop. Find the total time required for the journey.

Explanation:

Time during which there was acceleration = (v - u)  / a = 5 / 1.5 = 3.33 s

Time during which there was deceleration = (v - u)  / a = 5 / 2 = 2.5 s

Distance travelled during acceleration = 1 /2 a x t² = 1/2 x 1.5 x 3.33²

= 8.32 m

Distance travelled during deceleration = 1 /2 a x t² = 1/2 x 2 x 2.5²

= 6.25 m

Total distance travelled = 400 m

distance travelled when the velocity was uniform = 400 - ( 6.25 + 8.32 )

= 385.43 m

uniform velocity = 5 m /s

time  during uniform velocity existed

= 385.43 / 5 = 77.1 s

Total time required in the journey = 77.1 + 3.33 + 2.5

= 82.93 s

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