A level maths question

the total displacement is the area under the velocity/time graph, if you haven't tried that, then that's maybe where you should head towards lmao gl gl

A particle travels between three points on a line, P, Q and R. At t=0, the particle accelerated uniformly at 3 ms^-1 for 4 seconds, until it reaches Q with a velocity of U ms^-1. It then travels at this constant velocity for 6 seconds to point R. Immediately after passing R, the particle decelerates uniformly for T seconds until comes to rest.
a) Draw a velocity time graph for the particles motion
—> done
b) Find the value of U —> 27 ms^-1
c) Given that the total displacement is 405 m, find how long after passing P the particle comes to rest
d) Find the deceleration of the particle coming to rest


I’m struggling with part c and d... please help

Also, how did you calculate U?

V=u+ at
= 15+3*4
=27 ms^-1

Where did the initial velocity of 15 m/s come from as it wasn't mentioned in the original question?

Thanks!

Okay, so part c)...

Total displacement of the particle is 405m - as the particle has moved "forward" for its entire journey, displacement will be the distance between point P and when it comes to rest T seconds after it passes R. Do you know how to calculate displacement from a velocity-time graph?

It’s the area under the graph

Yes - so if you know this you should be able to figure out the total time of the journey. Which part are you struggling on?

You are told the area under the graph - use your diagram to find it using unknowns.

You don't need to use any of the suvat equations. Look at the area under the graph in terms of rectangles and triangles. Create an expression for the total area and equate this to 405. You should then be able to work out the value of T, and then the total time.

I tried it...

Where? There is a trapezium, a rectangle and a triangle.

Trap area = 1/2(15 + 27) x 4

Now try the other bits.

I got it... thank you so much 🙂

The total displacement is given as 405 m.... I need to find the time taken after the particle passes point P