Unlock M1 Level Question: Total Time to Travel 4 km

[CathyLou]

[SOLVED] M1 level help

Hi.

Could someone please help me with the following M1 level question? I would really appreciate any help as I am really stuck at the moment.

A car starts from rest at a point S on a straight racetrack. The car moves with constant acceleration for 20 s, reaching a speed of 25 m/s. The car then travels at a constant speed of 25 m/a for 120 s. Finally it moves with constant deceleration, coming to rest at a point F.

(a) Sketch a speed-time graph to illustrate the motion of the car.

I did this part.

The distance between S and F is 4 km.

(b) Calculate the total time the car takes to travel from S to F.

I wrote down:

4000 = (0.5 x 20 x 25) + 0.5(120 + (F - 20))x25 and this leads to 50F = 2500.

However, I am not sure if this is correct, or what to do next.

The correct answer is 200 seconds.

Thank you.

Cathy

 

[learningphysics]

Hi.

Could someone please help me with the following M1 level question? I would really appreciate any help as I am really stuck at the moment.

A car starts from rest at a point S on a straight racetrack. The car moves with constant acceleration for 20 s, reaching a speed of 25 m/s. The car then travels at a constant speed of 25 m/a for 120 s. Finally it moves with constant deceleration, coming to rest at a point F.

(a) Sketch a speed-time graph to illustrate the motion of the car.

I did this part.

The distance between S and F is 4 km.

(b) Calculate the total time the car takes to travel from S to F.

I wrote down:

4000 = (0.5 x 20 x 25) + 0.5(120 + (F - 20))x25 and this leads to 50F = 2500.

However, I am not sure if this is correct, or what to do next.

The correct answer is 200 seconds.

Thank you.

Cathy

When I solve your equation: 4000 = (0.5 x 20 x 25) + 0.5(120 + (F - 20))x25

I get F = 200.

 

[CathyLou]

Oh yeah - I get it now!

Thanks for your help!

Could someone please help me with the next part of the question too? I am completely stuck over what to do.

A motorcycle starts at S, 10 s after the car has left S. The motorcycle moves with constant acceleration from rest and passes the car at a point P which is 1.5 km from S. When the motorcycel passes the car, the motorcycle is still accelerating and the car is moving at a constant speed. Calculate

(c) the time the motorcycle takes to travel fro S to P,

(d) the speed of the motorcycle at P.

Thank you.

Cathy

 

[learningphysics]

Oh yeah - I get it now!

Thanks for your help!

Could someone please help me with the next part of the question too? I am completely stuck over what to do.

A motorcycle starts at S, 10 s after the car has left S. The motorcycle moves with constant acceleration from rest and passes the car at a point P which is 1.5 km from S. When the motorcycel passes the car, the motorcycle is still accelerating and the car is moving at a constant speed. Calculate

(c) the time the motorcycle takes to travel fro S to P,

(d) the speed of the motorcycle at P.

Thank you.

Cathy

Find the time at which the car reaches 1500m. call this tc. This is the same time that the motorcycle reaches 1500m. The time the motorcycle takes to go from S to P is just this tc - 10...

Then you can solve for the speed of the motorcycle, using the area under the v-t graph for the motorcycle... or just using your kinematics formulas... either way, you'll end up doing.

d = [(v1+v2)/2] *t

1500 = [(0 + v2)/2] * (tc-10)

d = (0 + v2)/2 * (

 

[CathyLou]

Thanks so much for your help!

Cathy