Kinematics help

[Chavi]

Hey forum,

I'm wondering if I can get some help with the following kinematics question:

1. A particle is brought to top speed with an accel which varies linearly as the distance travelled. It starts from rest with an accel of 3 m/s^2 and reaches top speed in a distance of 160m. Find:
a) the top speed
b) the speed when the particle has moved 80m

Thanks.

[98.40_for_sure]

Do you have the answers? I need something to check with, before i post up how i did it

[Martoman]

First one should be

Second

[Chavi]

First one should be

Second

According to the answers
a) 4sqrt(30) m/s
b) 6sqrt(10) m/s

[Martoman]

The way I got to the first one was:

let T be some time in the future at top speed x.

ie: a pretty triangle.



Also gradient of line is 3.







So x, top speed, = 320/10.33 = 30.98...

this assumes constant acceleration RTFQ

[Chavi]

my workings thus far have been:
when
so



so find that c =0, and:


now, how do you find k?

[Martoman]

Ok.

Simply you have

When x = 160, a = 0 as it accelerates no more!



Shove it in it works out to your answer for 1.

Then you have your v equation.

Shove in 80 for part 2.

Works out nicely.

[Chavi]

Ok.

Simply you have

When x = 160, a = 0 as it accelerates no more!



Shove it in it works out to your answer for 1.

Then you have your v equation.

Shove in 80 for part 2.

Works out nicely.

Thanks - i was experimenting with diff values - just overlooked the correct figure.