Direction matters
Christine Arron is a 100-m sprint athlete.
Immediately the starting pistol is fired,
Christine accelerates uniformly from rest,
reaching maximum velocity at the 50 m
mark in 4.16 s.
Her maximum velocity is 10.49 m s –1 .
Calculate her acceleration over the first
50 m of the race, showing full working.
Using the normal sign convection in which right is positive and left is
negative, by calculation her acceleration is +2.52 m s –2 . In this case, the
positive value means increasing velocity with time in the positive direction.
As she passes the finish line, Christine
begins to slow down.
She comes to rest in 8.20 s from a
velocity of 9.73 m s –1 .
Calculate her acceleration, showing full
working.
Using the normal sign convection in which right is positive and left is
negative, by calculation her acceleration is –1.19 m s –2 . In this case, the
negative value means decreasing velocity with time in the positive direction.
Before continuing you should give some thought to what els e a positive or
negative value of acceleration might mean.
OUR DYNAMIC UNIVERSE (H, PHYSICS)
© Learning and Teaching Scotland 2011
1
Consider Christine running in the
opposite direction, where the sign
convention remains the same.
What will a positive value of
acceleration mean in this case? What
about a negative value?
Immediately the starting pistol is fired, Christine accelerates uniformly from
rest, reaching maximum velocity at the 50 m mark in 4.16 s.
Her maximum velocity is –10.49 m s –1 (why is it negative?).
Calculate her acceleration over the first 50 m of the race, showing full
working.
Her acceleration is –2.52 m s –2 . The negative value indicates that she is
gaining speed in the negative direction.
As she passes the finish line, Christine begins to slow down. She comes to
rest in 8.20 s from a velocity of –9.73 m s –1 .
Calculate her acceleration, showing full working.
Her acceleration is a = 1.19 m s –2 . The positive value indicates that she is
losing speed in the negative direction.
When using equations in relation to motion, you must understand what t he
values mean. Remember, equations are just one way of describing motion –
you should develop a picture in your head of the actual motion being
described by the mathematics.
2
OUR DYNAMIC UNIVERSE (H, PHYSICS)
© Learning and Teaching Scotland 2011
Using the equations of motion: explaining good technique using an
example
Step 1: Write down the sign convention you are using for the situation.
Step 2: Write down what you know – think s s u v a t
s
s
u
v
a
t
sign convention (see step 1)
displacement
initial velocity
final velocity
acceleration
time
Step 3: Write down any other information you have, eg acceleration due to
gravity.
Step 4: Write down your formulae and check against data sheet. Select the
formula to use.
Step 5: Substitute values then rearrange the formula.
Step 6: Write answer clearly using magnitude wit h units and direction (if
appropriate).
Usain Bolt is a Jamaican sprinter and a three -time Olympic gold medallist.
Immediately the starting pistol is fired, Usain accelerates uniformly from
rest. He reaches 8.70 m s –1 in 1.75 s.
Calculate his displacement in this time.
OUR DYNAMIC UNIVERSE (H, PHYSICS)
© Learning and Teaching Scotland 2011
3
Example working
s  positive and  negative
s=?m
u = 0 m s –1 (this is an easy one to miss – the phrase to look for is ‘starting
from rest’)
v = 8.70 m s –1
a = ? m s –2
t = 1.75 s
Formulae
v  u  at
1
s  ut  at 2
2
2
2
v  u  2as
Can this be done in one calculation? Is there one formulae which links s, v, u
and t but does not require a?
On this occasion two formulae will be required, the first to determine
acceleration a and the second to calculate displacement s.
v = u + at
8.70 = 0 + a × 1.75
8.70 = 1.75a
a
8.70
1.75
a = 4.97 m s –2
then
1
s  ut  at 2
2
1
s  (0  t)   4.97  1.75 2
2
s  0  7.61
s  7.61m
4
OUR DYNAMIC UNIVERSE (H, PHYSICS)
© Learning and Teaching Scotland 2011
You should ensure that you are familiar with typical everyday velocities and
accelerations. This is key to understanding work in physics on motion. For
example, what is a realistic top speed for a world-class sprinter?
What sort of accelerations do you experience in everyday life? Do you
experience motion only in the horizontal? An accelerometer (a device which
measures acceleration in three dimensions) can be used to exp lore the
accelerations that you experience during everyday activities. Try it out – you
might be surprised by the results!
OUR DYNAMIC UNIVERSE (H, PHYSICS)
© Learning and Teaching Scotland 2011
5