Rectilinear Acceleration SS1 Physics Lesson Note

Acceleration

If a body changes its velocity with time, it is said to be accelerated. Acceleration is defined as the rate of change of velocity concerning time. Its unit is m/s².

Suppose a car moves with a particular velocity (u) and then it increases the velocity to (v) in the time interval (t), then the acceleration of the car is given by: a=v-u/t

If, on the other hand, the car slows down from v to u, the acceleration will have a negative value, which indicates deceleration or retardation.

Acceleration is a vector quantity.

Non-Uniform Acceleration

When the velocity of a moving body increases by an equal amount in equal intervals of time, no matter how small the time interval may be, it is said to move with uniform acceleration.

Acceleration Due To Gravity

Whenever a body falls freely, its velocity increases steadily from zero. In other words, the body accelerates. Conversely, when a body is thrown upwards, the speed decreases gradually until it comes to a stop (deceleration). This is because the earth attracts bodies close to it or on its surface. It has been estimated that the velocity of a body falling freely under gravity increases by about 9.8m/s² every second. In other words, the acceleration due to the gravitational pull of the earth has been estimated to be an average of 9.82m/s². This, however, may vary slightly as one moves from one location to another on the surface of the earth.

Equations of uniformly accelerated motion

1st Equation:

By definition, acceleration, a is given by:

a=v-u/t

Where:

v = final velocity

u = initial velocity

t = time taken to change from u to v

we can rearrange the equation above to become:

v = u + at

2nd Equation:

For a body whose speed changes from u to v, the average speed is given by:

u+v/2 

Now, distance S = average speed x time Therefore: Distance covered, S = (u+v/2)t

If we put v = u + at into the equation above, we have 

Distance covered S = (u+u+at/2)t S=(2u+at/2)t S=2ut/2 + at2/2 S = ut + 1½at2

3rd Equation:

If we square both sides of equation 1 and expand, we have

v2 = (u + at)2 or v² = u² + 2uat + a2t2 v2 = u² + 2a (ut + ½at²) v2 = u² + 2aS

Problem-Solving With The Equations

It is necessary for the student not only to commit the equations of motion to memory but also to be able to derive them. To solve problems successfully with the equations, take the following steps:

1. Identify all the (quantities) in a given problem. That is, you must know what u, v, a, t and s stand for.
2. You must be able to interpret the given problem of which of the quantities (u, v, a, t, s) are and which one of them is to be calculated.
3. Choose the equation that best connects the given quantities to the one you are to calculate.
4. Ensure all quantities are in S.I. units unless otherwise stated. That is for instance if speed is in km/h and time is in seconds (s), you should convert the unit of speed to m/s. Likewise, if the time given is given in minutes and velocity is given in m/s, the unit of time should be converted to seconds. Working with inconsistent units will give you the wrong solution to the problem.
5. Solve the equation for the unknown quantity.
6. Ensure the solution is expressed in the appropriate (or required) unit.