“In MATSEC Physics linear motion learning outcomes focus on using and applying the equations of linear motion, rather than requiring you to know how to derive them. Don’t worry, you won’t need to memorize complex derivations! Instead, you’ll learn how to effectively utilize these equations to solve various tasks and problems.
However, we understand that showing you the derivations can help enhance your mathematical skills and improve your understanding. It’s always great to have a strong foundation in math! This video covers the derivations in a way that is easy to follow and grasp.
The equations of linear motion describe the motion of an object in a straight line with constant acceleration. These equations are important in physics and are used to solve problems related to the motion of objects.
The first equation is v = u + at, where
– v is the final velocity,
– u is the initial velocity,
– a is the acceleration,
– t is the time taken.
This equation relates the final velocity of an object to its initial velocity, acceleration, and time.
The second equation is s = ut + 1/2at^2, where
– s is the displacement or distance traveled by the object
– u is the initial velocity,
– a is the acceleration,
– t is the time taken.
. This equation relates the distance traveled by an object to its initial velocity, acceleration, and time.
The third equation is v^2 = u^2 + 2as, which relates
– v is the final velocity,
– u is the initial velocity,
– a is the acceleration,
– s is the displacement or distance traveled by the object.
The forth equation is S = 1/2 (u+v) t, which relates
– v is the final velocity,
– u is the initial velocity,
– t is the time,
– s is the displacement or distance traveled by the object.
Examples of linear motions:
1. a car accelerating from rest
2. a ball thrown vertically upwards.
More examples:
- Define linear motion.
- What is the difference between distance and displacement?
- State the three equations of linear motion.
- A car starts from rest and accelerates at a rate of 4 m/s^2. How long will it take to reach a speed of 20 m/s?
- A ball is thrown vertically upward with an initial speed of 20 m/s. How high does it go?
- A car travels at a constant speed of 20 m/s for 10 seconds. What distance does it cover?
- A stone is dropped from a height of 100 meters. How long will it take to reach the ground?
Solutions:
- Linear motion is the movement of an object in a straight line.
- Distance is the total amount of ground covered by an object, while displacement is the shortest distance between the starting and ending positions.
- The three equations of linear motion are:
1. v = u + at (final velocity = initial velocity + acceleration x time)
2. s = ut + 0.5at^2 (distance = initial velocity x time + 0.5 x acceleration x time^2)
3. v^2 = u^2 + 2as (final velocity^2 = initial velocity^2 + 2 x acceleration x distance) - Using the first equation of linear motion, we can find the time taken:
v = u + at
20 = 0 + 4t
t = 5 seconds
Therefore, it will take 5 seconds to reach a speed of 20 m/s. - Using the third equation of linear motion, we can find the maximum height:
v^2 = u^2 + 2as
0 = 20^2 – 2 x 9.81 x s
s = 20.4 meters
Therefore, the ball will go up to a height of 20.4 meters. - Since the speed is constant, we can find the distance covered:
D = v x t
D = 20 x 10
s = 200 meters
Therefore, the car will cover a distance of 200 meters. - Using the second equation of linear motion, we can find the time taken:
s = ut + 1/2 at^2
100 = 0 x t + 1/2 x 9.81 x t^2
t = 4.52 seconds
Therefore, it will take 4.52 seconds to reach the ground.