Question

4. A train is travelling at a constant speed of 15 m/s. It starts to accelerate with an acceleration of 1 m/s2 for 3 seconds. What is the distance travelled by the train during the 3 seconds interval when it is accelerating?

Answer 1

do you know calculus

Answer 2

No, cause we are learning physics.

Answer 3

>.>

Answer 4

then you have to approximate with time intervals
For 1st second , the speed will increase from 15 to 16m/s
2nd second, increase from 16 to 17
3rd second, increase from 17 to 18

Answer 5

im not exactly sure on what method your teacher or class wants this to be done though

Answer 6

Alright. Then may i know what is the next step?

Answer 7

is tgis constant accelaration for 3 seconds?

Answer 8

if so we can use newtons equations for constant acceleration

Answer 9

ok pick a midpoint for each interval which we will use to approximate for the constant speed during a 1-sec interval.
1st second : 15.5
2nd second: 16.5
3rd second: 17.5

distance = rate*time, time is 1 for each case
Add those up to get distance

Answer 10

s = ut + 1/2 at^2
= =15*3 + 1.2 * 1 * 3^2
= 45 + 5.5
= 49.5 meters

Answer 11

agrees with dumbcow's answer

Answer 12

well yeah i could've used that too but it involved calculus to derive it

Answer 13

May i know why i get the answer if i add up the midpoint ?

Answer 14

And may i know what formula is this = ut + 1/2 at^2?

Answer 15

because say for 1st second, the speed is constantly changing right, however the acceleration is constant so if you take the speed right in the middle and apply to entire interval it captures all the changes. because early in the interval the speed is higher than actual but later on the speed will be lower than actual, they kind of cancel each other out.
hope that made some sense

Answer 16

Alright. Thank you !

Answer 17

these equations were developed using calculus as dumbcow said
they apply to motion at constant accekleration only
there are 4 main ones

s = (u + v )t / 2
v = u + at
s = ut + (1/2) at^2
v^2 = u^2 + 2as

where s = distance, u = initial velocity, v = final velocity, a = accelerartion, t=time

Answer 18

So actually , if the qn is asking for constant acceleration i can apply these four fomulas?

Answer 19

yes

Answer 20

they are very useful for falling objects where a = acceleration due to gravity

they are usually introduced in physics before calculus is taught ( in UK that is)