Any movement of bodies is studied by a special branch of physics - kinematics. It does not consider the causes that led to the beginning of the body’s movement, but studies only the laws of the change in the position of the body in space over time. In this article, we answer the question of how to find acceleration through speed.
Speed and acceleration - the main kinematic characteristics
Each student will be able to answer the question of what speed is. It is understood as a physical quantity that determines the speed with which the body travels distances, which is mathematically expressed through the derivative of the path l with respect to time t:
v = dl / dt.
In the SI system, speed is usually measured in meters per second (m / s).
If we now take the derivative with respect to time t of speed v, then we get the acceleration a:
a = dv / dt = d 2 l / dt 2 .
Note that the acceleration can also be calculated as the second time derivative of the path. The value of a shows the speed with which the value of v changes. Typically, acceleration is measured in meters per second squared (m / s 2 ).
Values a and v are vectorial. The speed is directed along the tangent to the trajectory, and the acceleration coincides with the velocity vector.
Equally accelerated (equally slow) movement in a straight line
When a body moves along a straight line with constant acceleration, that is, a = const, then there are only three formulas for determining acceleration through speed and time:
a = v / t;
a = (vv 0 ) / t;
a = (v 0 -v) / t.
The first expression allows you to determine the acceleration if the body began an accelerated motion from a state of rest. It differs from the mathematical definition of acceleration in that, in this case, the average value of a is determined for the time t. The second expression is also valid for accelerated motion, only in this case, before the occurrence of acceleration, the body already had a speed v 0 . Finally, the third formula is applied when the body slows down (slows down) with constant acceleration.
Note that all three equalities assume a linear relationship between a and v.
Problem solving example
The car moved along the highway at a speed of 80 km / h. Then he began to slow down and stopped exactly 1 minute later. It is necessary to determine its average braking acceleration.
Before using the acceleration through velocity formula recorded in the previous paragraph, we convert the quantities known from the problem condition to SI units:
v 0 = 80 km / h = 22.22 m / s;
t = 1 min = 60 s.
Since the car finally stopped, then v = 0. Substitute all the known values in the corresponding formula, we get:
a = (v 0 -v) / t = 22.22 / 60 = 0.37 m / s 2 .
The calculated value is not too large compared to the acceleration that our planet tells all bodies (9.81 m / s 2 ).