Question

The Driver of a vehicle on a level road determined that she could increase her speed from rest to 50 mi/h in 12.8 sec and from rest to 65 mi/h in 19.8 sec. If it can be assumed that the acceleration of the vehicle takes the form: (du/dt) = (alpha) - (beta)*(u(t)) Determine the maximum acceleration of the vehicle.

Answer 1

maximum acceleration is 1.746 m/s²

Step-by-step explanation:

given data

`(du)/(dt)` = (α) - (β) ×(u(t))

speed = rest to 50 mi/h = 22.352 m/s

time = 12.8 sec

speed = rest to 65 mi/h = 29.05 m/s

time = 19.8 sec

solution

we get here maximum acceleration of vehicle that is

maximum acceleration =
`((du)/(dt) )/(t)`

maximum acceleration =
`(v1-V2)/(t)` ...............1

put here value

maximum acceleration =
`(22.352-0)/(12.8)`

maximum acceleration = 1.746 m/s²

and for another vehicle

maximum acceleration =
`(29.05-0)/(19.8)`

maximum acceleration = 1.46 m/s²

so here maximum acceleration is 1.746 m/s²