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1. Hi, I have the following questions.

1. A car accelerates uniformly from rest along a straight road and experiences negligible frictional forces. The car travels 15m in the second second of its journey. How far does it travel in the fifth second? (OPTIONS: 15m, 35m, 45m, 75m)

2. A car passes through traffic lights as they turn from red to green at a speed of 12ms-1. A motorcyclist, starting from rest, accelerates from the traffic lights in the same direction as the car at 1.5ms-2. After what distance from the light will they meet. (OPTIONS: 16m, 120m, 168m, 192m) NOTE - assume the car has constant accleration.

I can derive the following information from question 2, but I am stuck as to what to do from thereon. u = 0, a = 1.5.

Update - I have got question 1 to being 45m.
2. (Original post by nwmyname)
Hi, I have the following questions.

1. A car accelerates uniformly from rest along a straight road and experiences negligible frictional forces. The car travels 15m in the second second of its journey. How far does it travel in the fifth second? (OPTIONS: 15m, 35m, 45m, 75m)

2. A car passes through traffic lights as they turn from red to green at a speed of 12ms-1. A motorcyclist, starting from rest, accelerates from the traffic lights in the same direction as the car at 1.5ms-2. After what distance from the light will they meet. (OPTIONS: 16m, 120m, 168m, 192m) NOTE - assume the car has constant accleration.

I can derive the following information from question 2, but I am stuck as to what to do from thereon. u = 0, a = 1.5.

Update - I have got question 1 to being 45m.
s=(u+v)/t

for the second second u=v/2 (because constant acceleration)

from which you can get u and hence a... which leads you to a solution
3. sorry - wrong one

for the car & bike you're looking for the point at which they're the same distance from the lights at the same time.

using suvat, you can write equations for s for both vehicles as a function of t and find the time till they pass by treating as simultaneous equations... then it's easy to find out how far either of them has travelled in that amount of time (but slightly easier for the car)
4. Joinedup I have finally solved it - at least I think so.

The Car
S
U 12
V
A 0
T

The Motorbike
S
U 0
V
A 1.5
T

Using the Car
s = ut + 1/2 at^2
s = ut (as a = 0)
s = 12t

Using the Motorbike
s = ut + 1/2 at^2
s = 1/2 at^2 (as u = 0)
s = 1/2 (1.5) t^2
s = 0.75 t^2

Subsitute the first equation to the second
12t = 0.75t^2
12t - 0.75t^2 = 0
t (12 - 0.75t) = 0
t = 0 (1)
12 - 0.75t = 0
12 = 0.75t
16 = t [so the time is 16 seconds]

The car travels at constant velocity of 12ms-1 so to find the distance, using speed x time, I do 12 * 16 = 192.
Is this correct?
5. (Original post by nwmyname)
Hi, I have the following questions.

1. A car accelerates uniformly from rest along a straight road and experiences negligible frictional forces. The car travels 15m in the second second of its journey. How far does it travel in the fifth second? (OPTIONS: 15m, 35m, 45m, 75m)

2. A car passes through traffic lights as they turn from red to green at a speed of 12ms-1. A motorcyclist, starting from rest, accelerates from the traffic lights in the same direction as the car at 1.5ms-2. After what distance from the light will they meet. (OPTIONS: 16m, 120m, 168m, 192m) NOTE - assume the car has constant accleration.

I can derive the following information from question 2, but I am stuck as to what to do from thereon. u = 0, a = 1.5.

Update - I have got question 1 to being 45m.
You use s = ut + 1.at^2 for number 2 (methinks)
6. (Original post by nwmyname)
Hi, I have the following questions.

1. A car accelerates uniformly from rest along a straight road and experiences negligible frictional forces. The car travels 15m in the second second of its journey. How far does it travel in the fifth second? (OPTIONS: 15m, 35m, 45m, 75m)

2. A car passes through traffic lights as they turn from red to green at a speed of 12ms-1. A motorcyclist, starting from rest, accelerates from the traffic lights in the same direction as the car at 1.5ms-2. After what distance from the light will they meet. (OPTIONS: 16m, 120m, 168m, 192m) NOTE - assume the car has constant accleration.

I can derive the following information from question 2, but I am stuck as to what to do from thereon. u = 0, a = 1.5.

Update - I have got question 1 to being 45m.
I got 45 for the first one too, as for the second one, I think you are correct in your method with the simultaneous equation
7. (Original post by nwmyname)
Joinedup I have finally solved it - at least I think so.

The Car
S
U 12
V
A 0
T

The Motorbike
S
U 0
V
A 1.5
T

Using the Car
s = ut + 1/2 at^2
s = ut (as a = 0)
s = 12t

Using the Motorbike
s = ut + 1/2 at^2
s = 1/2 at^2 (as u = 0)
s = 1/2 (1.5) t^2
s = 0.75 t^2

Subsitute the first equation to the second
12t = 0.75t^2
12t - 0.75t^2 = 0
t (12 - 0.75t) = 0
t = 0 (1)
12 - 0.75t = 0
12 = 0.75t
16 = t [so the time is 16 seconds]

The car travels at constant velocity of 12ms-1 so to find the distance, using speed x time, I do 12 * 16 = 192.
Is this correct?
I got 192... though it's pretty straightforward to verify for yourself.

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