Question

what do you mean by acceleration? How do you find acceleration from time - velocity graph? ​

Answer 1

Answer:

by considering the velocity versus time graph below.

The line is sloping upwards to the right. But mathematically, by how much does it slope upwards for every 1 second along the horizontal (time) axis? To answer this question we must use the slope equation.

Explanation:

The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. A method for carrying out the calculation is

Pick two points on the line and determine their coordinates.

Determine the difference in y-coordinates for these two points (rise).

Determine the difference in x-coordinates for these two points (run).

Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

The calculations below shows how this method can be applied to determine the slope of the line. Note that three different calculations are performed for three different sets of two points on the line. In each case, the result is the same: the slope is 10 m/s/s.

 

For points (5 s, 50 m/s) and (0 s, 0 m/s):

Slope = (50 m/s - 0 m/s) / (5 s - 0 s) = 10 m/s/s

 

 

For points (5 s, 50 m/s) and (2 s, 20 m/s):

Slope = (50 m/s - 20 m/s) / (5 s - 2 s) = 10 m/s/s

 

For points (4 s, 40 m/s) and (3 s, 30 m/s):

Slope = (40 m/s - 30 m/s) / (4 s - 3 s) = 10 m/s/s

 

Observe that regardless of which two points on the line are chosen for the slope calculation, the result remains the same - 10 m/s/s.

Answer 2

Answer:

Acceleration of a body is defined as the rate of change of its velocity with time.

For any v-t graph the acceleration is the slope of the graph. For average acceleration in a time period ‘t’ consider the change in velocity in time t and divide it by the time t. For instantaneous acceleration you need to go into the realm of differential calculus. You do the same process as above and then reduce the time period to infinitely short length. This gives you the instantaneous acceleration at that particular instant of time. Consider the graph below for greater clarity —