2. SPEED, VELOCITY AND ACCELERATION

1.2 SPEED

Speed is defined as distance moved by an object per unit time. It is a scalar quantity and is measured in metre per second (m/s or ms-1).

1.2.1 VELOCITY

Velocity is defined as distance travelled in a specified direction per unit time.

OR

Velocity is defined as displacement over time. It is a vector quantity and is also measured in metre per second (m/s or ms-1).

Both speed and velocity have the same unit, formula and dimension.

v = s/t

where v = velocity(speed) in m/s

s = displacement (distance) in m

t = time in seconds.

Examples on speed and velocity

1. A car has a velocity of 72km/hr. How far does it travel in ½ minute?

2. A student walks a distance of 3km in 20 minutes. Calculate his average speed.

3. A man cycles non-stop through a distance of 1.0km in 5minutes. Calculate his average speed.

1.2.3 RECTILINEAR ACCELERATION

The term rectilinear acceleration means the rate of increase of velocity along a straight-line path in a unit time. When the velocity of an object changes it could be said to accelerate or decelerate. Acceleration is defined as the increasing rate of change of velocity with time. Deceleration on the other hand is defined as the decreasing rate of change of velocity with time.

Deceleration is also called retardation or negative acceleration.

Acceleration (Deceleration) = Change in velocity

Time taken for change 

= Final velocity - Initial velocity

        Final time - Initial time

 1.2.4 EQUATIONS OF UNIFORMLY ACCELERATED MOTION

Equations of motion for a body traveling along a straight line with uniform acceleration are as follows:

v = u + at --------------------(1)

s = ut + ½ at2 --------------------(2)

v2 = u2 + 2as ---------------(3)

1.2.5 ALW AYS REMEMBER:

1. When an object moves or accelerates from rest, its initial velocity, u = 0.

2. When a body comes to rest or stops, its final velocity, v = 0.

3. When a body’s velocity is constant or not changing, its acceleration, a = 0.

Examples

1.   A particle accelerates uniformly from rest at 6.0m/s2 for 8s and then decelerates uniformly to rest in the next 5s. Determine the magnitude of the deceleration. 

2. A body accelerates uniformly from rest at the rate of 3ms-2 for 8s. Calculate the distance covered by the body during acceleration.

3. If a car starts from rest and moves with a uniform acceleration of 10m/s2 for 10s. What is the distance it's covers in the last 1sec of the motion?

4. A bus driver moving at a velocity of 100km/hr suddenly sees a Goat crossing the Highway 49m ahead. He hit hand on his brakes to get a maximum retardation of 8.0ms-2

a. How far does he go before stopping?

b. Can he avoid hitting the Goat?