Linear Motion Calculation 2

Linear motion calculation 2

A bike has to move along a straight road. It starts from rest and then moves with uniform acceleration. After moving a distance of 100 m, it achieves a velocity of 120 m s^-1.

Find:

a) the bike acceleration
b) the time taken
c) the bike's velocity when t= 3s

SOLUTION

For question A)

Extract all the information that are needed.

u = 0 m/s
v = 120 m/s
s =100 m

What you need to find is the acceleration.

However there are several linear motion equation that needs to be considered.

1. a = (v -u)/t

2. s = 1/2 (u +v) t

3. s = ut + 1/2(at^2)

4. v^2 = u^2 + 2as

So we choose this equation v^2 = u^2 + 2as, because we have v, u and s.

rearrange the equation, we will get

a =  (v^2 - u^2)/2s

= (120^2 - 0^2) / 2 (100)

= 72 m/s^2


For question B)

using a = (v - u) / t

rearrange the equation and you will get

t = (v -u)/ a

= (120 -0) / 72

= 5/3 s


For question C)

we need to find v,

so the equation that is most suitable is

v = u + at

= 0 + 72 (3)

= 216 m/s


Hope everything makes sense!

Linear Motion Calculation Examples

A bicycle moved from point A and then moved 50 m to the north in 60 seconds. The bicycle then moved 120 m to the east in 40 seconds. Finally, it stopped. Calculate the

1. Total distance moved by the bicycle
2. Displacement
3. Velocity
4. Average speed
5. Speed of the bicycle when it is moving to the north

Solution:

1. Total distance = 50m + 170m
                          = 170m

2. Displacement

Remember displacement is the shortest distance between two points.

Imagine A as the beginning of a triangle.  Then connect it with a line of 50m upwards then it turns left 120m (go east). so the distance is the hypotenuse.

Using Pythagoras' theorem = Squared root (120^2 + 50^2)
                                         = 130m

3. Velocity = Displacement / time

= 130 m / 100 s
= 1.3 m s^-1

4. Average speed of the bicycle = total distance / total time

= 170m/ 100s
= 1.7 m s^-1

5. Speed = distance / time

Distance = 50m, time = 60s

= 50m / 60s

= 0.83 ms^-1

Be careful during calculation as most of the time Physics requires a good skill in maths!!

Distance, Displacement, Velocity, Speed and Acceleration

Distance and Displacement

Distance is the total path length traveled from one location to another. It is a scalar quantity.

Displacement is the distance between two locations measured along the shortest path connecting them, in specified location. It is a vector quantity. The SI unit of distance and displacement is metre (m).

Speed and Velocity

Speed is the distance traveled per unit time or the rate of change of distance.

Speed = total distance traveled / time taken

Velocity is the speed in a given direction or the rate of change of displacement.

Average velocity = displacement/ time taken

Acceleration and Deceleration

Acceleration is the rate of change of velocity.

Acceleration = change of velocity / time taken

Change of velocity = final velocity (v) – initial velocity (u)

Acceleration = (final velocity – initial velocity) / time taken
  = (v – u) / t

Things to remember:

1. Constant velocity means the object is not accelerating. Acceleration is zero.
2. Constant acceleration means the object is increasing its velocity.