Mechanics 1 small question!

Hello, just a small mechanics 1 question..

A car rounds a bend at 10m/s , and then accelerates at 0.5 m/s along a straight stretch of road. There is a T-junction 400m from the bend. When the car is 100m from the T-junction, the driver brakes and brings the car to rest at the junction with constant deceleration. Find how fast the car is moving when the brakes are applied, and the deceleration needed for the car to stop at the junction.

Thanks a lot
From John

Reply 1

vector

Ok. Have you drawn diagrams - do it in stages. If you're really stuck:

Try again before reading the below

For acceleration:

s=300m
a=0.5ms^-2
u=10m/s
v=?

v^2=u^2+2as = 400

v=20

For decelleration,

u=20
a=?
v=0
s=100

v^2=u^2+2as

0=400 + 200a

200a=-400

Unparseable latex formula:

a=-2ms^{-2**

Reply 2

Eddie K

First, always draw a picture to describe the problem - see attached diagram.

After studying the diagram, it is clear you have enough information to work through the problem straight away. So:

Applying v² = u² + 2as from A to B to find the velocity at B, taking right as positive:

v² = u² + 2as
v² = 10² + (2 x 0.5 x 300)
v² = 400
v = 20 m/s

Applying v² = u² + 2as from B to C to find the decceleration required to stop at C, taking right as positive:

v² = u² + 2as
0 = 20² + (2 x a x 100)
0 = 400 + 200a
-400 = 200a
a = -2 m/s²

As you can see this isn't a difficult question. If you're getting stuck, draw a picture, they always help. Jot down what information you know, as I did, and see what equations you can use. Don't try and do everything in your head.

Diagram.GIF4.3KB

Reply 3

Neo1

Oh right thanks a lot, I managed to do all the working out..

I have another question which I dont understand:

A motorist travelling at u m/s joins a straight motorway. On the motorway she travels with a constant acceleration of 0.07 m/s until her speed has increased by 2.8 m/s.

(a) Calculate the time taken for this increase in speed (THIS ONE IVE DONE)

(b) Given that the distance travelled while this increase takes place is 1050m, find u.

Thanks a lot
From John

Reply 4

GarethBrown

s= ut + 0.5 at

^2

So:

u = (s-0.5at

^2

)/t

You get given a and s, and you worked out t in part a), so the only variable left is u. You need to find the correct suvat equation from your armoury and then just manipulate it to make the unknown the subject (u in this case)

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