hello students let us now continue our discussion in straight line motion [Music] i am going to explain to you the difference between the average and instantaneous speed average and instantaneous velocity and average and instantaneous acceleration the most essential learning competency for this lesson is to convert a verbal description of a physical situation involving uniform acceleration in wide one dimension into a mathematical description average speed is a scalar quantity that refers to the rate at which an object covers a distance to compute the value of average speed we will use the formula length of path that is the distance divided by time the unit for the average speed is equal to meter per second average velocity is a vector quantity that refers to the rate at which the object changes its position to compute the value of the average velocity we will use the formula displacement divided by time please take note that displacement is a vector quantity that is equal to x sub 2 minus x sub 1. the unit for the average velocity is equal to meter per second instantaneous speed is defined as the measure of how fast a particle is moving it is the speed of the object at any given instant but the question is how long is an instant in physics this refers to a single value of time it has no duration at all instantaneous velocity measures how fast a particle is moving and in what direction it is moving take note it is a vector quantity we need to consider the direction this is an example please take note that the instantaneous speed is the magnitude of the instantaneous velocity and so instantaneous speed can never be negative the instantaneous velocity is the limit of the average velocity as the time interval approaches to zero it equals the instantaneous rate of the change of position with time the delta t is always positive instantaneous velocity has the same algebraic as displacement a positive value of v sub x means that x in increasing the motion is in the positive x direction a negative value v sub x means that x in decreasing the motion is in the negative x direction average acceleration is a vector quantity that defined as the change in velocity divided by time interval at which the change occurs instantaneous acceleration is the limit of the average of the acceleration as the time interval approaches to zero in calculus instantaneous acceleration equals the instantaneous rate of change of velocity with time let's have a short quiz question number one study the motion in each case one a tricycle moving at 50 meter per second in a straight path two a track moving on a straight road and then slowing down to stop three a motorcycle initially moving at 80 meter per second north eastward and then 60 meter per second is ward 4 a bus moving at 75 meter per second around the curve which bodies moves with constant speed letter a 3 and 4 only b 1 and 4 only c 2 and 3 only d 2 3 and 4 only the right answer is letter b one and four only example problem number one a car moving along the x axis has a velocity that varies in time according to the equation v is equal to 40 minus 5 t squared meter per second where t is in seconds compute the average acceleration in the time interval t is equal to 0 and t is equal to 2.0 seconds average acceleration is equal to the change in x component of velocity divided by the time interval delta t the velocity at this sub i or the initial velocity is equal to t sub a that is equal to zero and then the t final which is equal to t sub b is equal to 2 seconds by substituting these values of t into the expression for the velocity v sub a is equal to 40 minus 5 multiplied by 0 raised to 2 therefore v sub a is equal to positive 40 meter per second v sub b is equal to 40 minus 5 multiplied by 2 squared plus 20 meter per second that is equal to 20 meter per second acceleration is equal to v sub b minus v sub a divided by t sub b minus t sub a that is equal to 20 minus 40 meter per second divided by 2 minus 0 second that is equal to negative 10 meter per second example problem number two the x velocity of a jeepney at any given time t is given by the equation v is equal to 40 meter per second plus 0.5 meter per cubic second t squared derive an expression for the instantaneous x acceleration and any time and use it to find the x acceleration at t is equal to 3 seconds to solve this problem take the derivative of the expression for b with respect to t the derivative of constant is 0 and the derivative of t squared is 2t therefore the expression for a is equal to 1.0 meter per cubic second multiplied by t when t is equal to three second a is equal to three meter per second squared okay our next topic will be about graph it will be continued on our next lesson okay thank you