In A2/A-Level Mathematics, we discussed the equation of motion in part 1 and now we will have some examples.

__Example #1__

A car starts from rest and accelerates at 10 ms^{-1} for 3 secs. What is the maximum speed it attains?

__Example #2__

A car travelling at 25 ms^{-1} starts to decelerate at 5 ms^{-2}. How long will it take for the car to come to rest?

__Example #3__

A car travelling at 20 ms^{-1} decelerates at 5 ms^{-2}. How far will the car travel before stopping?

__Example #4__

A car travelling at 30 ms^{-1} accelerates at 5 ms^{-2} for 8 secs. How far did the car travel during the period of acceleration?

Vertical motion under gravity

In A2/A-Level Mathematics, these problems concern a particle projected vertically upwards and falling 'under gravity'. In these types of problem it is assumed that:

air resistance is minimal

displacement & velocity are positive(+) upwards & negative(-)downwards

acceleration(g) __always__ acts downwards and is therefore negative(-)

acceleration due to gravity(g) is a constant

__Example #1__

A stone is thrown vertically upwards at 15 ms^{-1}.

i) what is the maximum height attained?

ii) how long is the stone in the air before hitting the ground?

i) (Assume g = 9.8 ms^{-2}. Both answers to 2 d.p.)

ii)

__Example #2__

A boy throws a stone vertically down a well at 12 ms^{-1}. If he hears the stone hit the water 3 secs. later,

i) how deep is the well?

ii) what is the speed of the stone when it hits the water?

i)

(Assume g = 9.8 ms^{-2}. Both answers to 1 d.p.)

ii)

That's the end of the topic in A2/A-Level Mathematics.