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

Answer:

maximum acceleration is  1.746 m/s²

Explanation:

given data

$\frac{du}{dt}$ = (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 = $\frac{\frac{du}{dt} }{t}$

maximum acceleration = $\frac{v1-V2}{t}$    ...............1

put here value

maximum acceleration = $\frac{22.352-0}{12.8}$

maximum acceleration = 1.746 m/s²

and for another vehicle

maximum acceleration = $\frac{29.05-0}{19.8}$

maximum acceleration = 1.46 m/s²

so here maximum acceleration is  1.746 m/s²