By one dimension we mean that the body is moving only in one plane and in a straight line.
Like if we roll a marble on a flat table, and if we roll it in a straight line (not easy!), then it would be undergoing one-dimensional motion.
There are four variables which put together in an equation can describe this motion. These are Initial Velocity (u); Final Velocity (v), Acceleration (a), Distance Traveled (s) and Time elapsed (t). The equations which tell us the relationship between these variables are as given below.
v = u + at
v2 = u2 + 2as
s = ut + 1/2 at2
average velocity = (v + u)/2
Of course, these equations are applicable only if acceleration is constant
Armed with these equations you can do wonderful things like calculating a cars acceleration from zero to whatever in 60 seconds !!
A cyclist speeds up at a constant rate from rest to 8 m/s in 6s. Find the acceleration of the cyclist.
u = 0 m/s [body starts from rest]
v = 8 m/s
t = 6 s
v = u + at
=> a = (v-u)/t = (8-0)/6 = 4/3 m/s2 = 1.33 m/s2
An electron has a constant acceleration of 3.2 m/s2. At a certain instant its velocity is 9.6 m/s. What is its velocity 2.5 seconds earlier?
a = 3.2 m/s2
v = 9.6 m/s
u = ?
t = 2.5 s
v = u + at
=> u = v - at = 9.6 -3.2 x 2.5 = 1.6 m/s2
A racing car reaches a speed of 50 m/s. At this instant it begins a uniform negative acceleration using a parachute and a braking system and comes to rest 50 s later. How far does the car travel after acceleration starts.
u = 50 m/s
v = 0 m/s
t = 50 s
Here we have two unknowns 's' and 'a'. So first we will find 'a' using v = u + at.
0 = 50 + a x 5
=> 0 = 50 + 5a
=> a = -50/5 = -10 m/s2
Now, we find the distance travelled
S = ut + 1/2 at2
= 50 x 5 + 1/2 x (-10) x 52)
= 250 -125 = 125 m
A car brakes from a speed of 108 km/h to 72 km/h duing a displacement of 100m. What is its acceleration?
We write down the given data and make the units consistent. All the units should be in SI
u = 108 km/h = 108 x 1000/(60 x 60) = 108 x 5/18 = 30 m/s
[1 km = 1000 m and 1 h = 60 x 60 = 3600 s]
v = 72 km/h = 72 x 5/18 = 20 m/s
s = 100 m
v2 - u2 = 2as
=> a = (v2 - u2)/(2 x 100) = (400 - 900)/(2 x 100) = -2.5 m/s2