Lecture 6: Constant acceleration
Example 1:
A bicyclist pedaling along a straight road at 25 km/h uniformly accelerates at
+3.00 ms !! for 3.00 s. Find her final speed.
Solution:
Write down the values we know and the value we want:
25
𝑣! = 25 km h!! =
ms !! = 6.94 m s !!
3.6
𝑎 = +3.00 ms !!
𝑡 = 3.00 s
𝑣! = ?
Use equation 1, which involves 𝑣! , 𝑣! , 𝑎 and 𝑡:
𝑣! = 𝑣! + 𝑎𝑡
m
m
= 6.94 + 3.00 ! ×3.00 s
s
s
= 6.94 + 9.00 = 15.94 ms !! = 57.4 km h!!
Example 2:
The fastest animal sprinter is the cheetah, reaching speeds in excess of 113 km/h. These
animals have been observed to bound from a standing start to 72 km/h in 2.0 s.
(a) What is the cheetah’s acceleration (assuming it is constant)?
(b) Using this acceleration, what minimum distance is required for the cheetah to go
from rest to 20 m/s?
Solution:
(a) We are given
𝑣! = 0 km h!!
𝑣! = 72 km h!! =
72
ms !! = 20 m s !!
3.6
𝑡 = 2 s
𝑎 = ?
so use equation 1 again. Re-arrange to find a:
𝑣! − 𝑣! 20 − 0
𝑎=
=
= 10 ms !!
𝑡
2
(b) To find the distance, we can use either equation 2 or equation 3. Using equation 2:
!
𝑑 = 𝑣! 𝑡 + !𝑎𝑡 !
!
Or using equation 3:
= 0 + !×10×2! = 20 m
𝑣! ! = 𝑣! ! + 2𝑎𝑑
so
𝑣! ! − 𝑣! !
2𝑎
20! − 0
=
= 20 m
2×10
so either equation gives the correct answer
𝑑=
Example 3:
A ball is dropped from the roof of a building. If the building is 100 m high,
(a) At what speed will the ball hit the ground?
(b) How long will the ball take to reach the ground?
(c) How would these results change if the ball is thrown downwards at 10.0 m/s?
Solution:
(a) We are given
𝑑 = −100 m
𝑎 = −9.8 ms !! (because the ball is falling under gravity)
𝑣! = 0
𝑣! = ?
Use equation 3:
𝑣! ! = 𝑣! ! + 2𝑎𝑑
= 0 + 2×−9.8×−100 = 1960
so
𝑣! = 1960 = 44.3 ms !! = 160 km h!! (b) We know d, a and 𝑣! , and we want to know t, so use equation 2:
!
𝑑 = 𝑣! 𝑡 + !𝑎𝑡 !
so
!
−100 = 0 + ! × −9.8 × 𝑡 ! so
2×100
𝑡! =
= 20.4
9.8
so
𝑡 = 20.4 = 4.5 s
(c) If the ball is thrown downwards at 10 m s !! , then 𝑣! = −10 m s !! , and we use
equation 3 again:
𝑣! ! = 𝑣! ! + 2𝑎𝑑
= (−10)! + 2×−9.8×−100 = 100 + 1960 = 2060
so
𝑣! = 2060 = 45.3 ms !!