please help me with this

Question

bus starts from rest at point A (figure 1) and accelerates at the rate of 0.8

m/s2 until it reaches a speed of 12 m/s. It then proceeds at 12m/s until the

brakes are applied; it comes to rest at point B, 42 meters beyond the point

where the brakes were applied. Assuming uniform deceleration and knowing

that the distance between A and B is 300 meters, determine the time required

for the bus to travel from A and B.

Answer 1

Hello Des -

Happy to help!

Whenever the acceleration changes you must begin a new "part" of the problem - so there are 3 "parts" to this. Also, the final velocity for each "part" becomes the initial velocity for the next "part".

Find the time for each of the 3 parts and add them to obtain the answer.

Part 1: Use v_f = v_i + at --> 12 = 0 + 0.8t₁ Solve for t₁.

Part 2: Use x = 1/2at² + v_it --> ? = 1/2(0)t₂² + 12t₂ Oops, we need x₂!

To find x₂: subtract (x₁ + x₃) from 300m. From the given info we already know that x₃ = 42m.

To find x₁ substitute t₁ into: x = 1/2at² + v_it --> x₁ = 1/2(0.8)t₁² + 0t₁ Solve for x₁.

Now substitute x₁ into: x₂ = 300 - (x₁ + x₃) --> x₂ = 300 - (x₁ + 42) Solve for x₂.

Go back to the original set-up and substitute x₂ into it: x₂ = 1/2(0)t₂² + 12t₂ Solve for t₂.

Part 3: Use v_f = v_i + at --> 0 = 12 + ?t₃ Oops, we need a₃, let's find it:

Use v_f² = v_i² + 2 ax --> 0² = 12² + 2a₃42 Solve for a₃.

Substitute a₃ into our first attempt: 0 = 12 + a₃t₃ Solve for t₃.

Now you can answer the question: The time required for the bus to travel from A and B = t₁ + t₂ +t₃.

There it is! :-)

Remember: When acceleration changes. a new "Part" of the problem begins. Also: v_f(previous) = v_i(next).

Answer 2

Hi

There is three steps ( not in time order)

1- first one ,accelerated , v_i = 0 , v_f= 12 m/s, a=0.8 m/s², find (t) from v_f= v_i +at ,

Then find d₁ from ( v_f)² = (v_i)²+2a x ,x=d.

3- last one , accelerated , v_i = 12 m/s,

v_f= 0 m/s , (d₃ )= x= 42 m , find (a ) using

(v_f)² = ( v_i )²+ 2ax ,

then find ( t ₃) from

v_f = v_i + at .

2- uniform motion ( constant speed ) middle step. v= 12 m/s , x₂=?

X₂ = 300 - ( d₁ + 42) =#.

Use x=v.t ,to find t₂ by dividing ( # / 12 )

_{Now you can find the total time which =} t₁+ t₂ + t₃