The Student Room Group

Variable Acceleration

A sled is moving down a steep hill in a straight line. At the time t s, the acceleration of the sled is a m s^-2 where a=1/500(20t^2-t^3), t is larger than or equal to 0, and smaller or equal than to 20. When t=0 the sled is at rest at the top of the hill. Find the distance the sled travels in the first 10s of its motion.
So what do I do? Do I just sub in 0 and 10 for t? Or is it something else?
Reply 1
How is acceleration related or transformed to displacement?
Hint - velocity is a halfway house.
Reply 2
Acceleration is related to displacement, because I need to find acceleration to be able to find displacement? Since the equation S=ut 0.5at^2So how do I start of though? Sub in 10 for t in the equation given? That would be a=1/500(2000-1000) which equals to acceleration is 2ms^-2
Reply 3
Original post by Jon Cheung
Acceleration is related to displacement, because I need to find acceleration to be able to find displacement? Since the equation S=ut 0.5at^2So how do I start of though? Sub in 10 for t in the equation given? That would be a=1/500(2000-1000) which equals to acceleration is 2ms^-2

There us a relation using calculus.
You must have covered it on your A level?
Reply 4
Original post by mqb2766
There us a relation using calculus.
You must have covered it on your A level?

integrate twice?
Reply 5
Original post by effg04
integrate twice?

Yes, I was hoping the OP would realise this.
Original post by mqb2766
Yes, I was hoping the OP would realise this.

so integrate twice, then what? I know you have to sub in t=0 s=0 but what second set of values do I use to find the constants from the integration before substituting in t=10 to find the distance
Reply 7
Original post by RoutneClient77
so integrate twice, then what? I know you have to sub in t=0 s=0 but what second set of values do I use to find the constants from the integration before substituting in t=10 to find the distance

You integrate once to get velocity then again to get distance or displacement. So you have initial conditions in each case.

Note its better to start your own thread rather than bump an old one.
(edited 4 months ago)
Original post by mqb2766
You integrate once to get velocity then again to get distance or displacement. So you have initial conditions in each case.

Note its better to start your own thread rather than bump an old one.

i did it by finding a = 2. and got the answer s=100m is that correct?
Original post by mqb2766
You integrate once to get velocity then again to get distance or displacement. So you have initial conditions in each case.

Note its better to start your own thread rather than bump an old one.

oh mb ill make a new post about it

Quick Reply

Latest