Acceleration and speed are two important kinematic characteristics of any type of movement. Knowing the dependence of these quantities on time allows us to calculate the path traveled by the body. This article answers the question of how to find acceleration, knowing the speed and time.
The concept of speed and acceleration
Before giving an answer to the question of how, knowing the speed and time, to find the acceleration, we consider each of the characteristics from the point of view of physics.
Velocity is the quantity that determines the speed of change of coordinates in space when the body moves. The speed is calculated by the formula:
v = dl / dt.
Where dl is the path traveled by the body during dt. Speed ββis always directed along the tangent in the trajectory of movement.
Movement can occur either with a constant speed in time, or with a variable. In the latter case, they speak of the presence of acceleration. In physics, acceleration determines the rate of change of v, which is written in the form of a formula as follows:
a = dv / dt.
This equality is the answer to the question of how to find acceleration in speed. To do this, it is enough to take the first time derivative of v.
The direction of acceleration coincides with the direction of the difference of the velocity vectors. In the case of rectilinear accelerated motion, the quantities a and v are directed in the same direction.
How to find acceleration, knowing speed and time?
When studying mechanics, the uniform and uniformly accelerated types of motion along a straight path are first considered. In both cases, to determine the acceleration, you should choose the time interval Ξt. Then, it is necessary to determine the values ββof the speeds v 1 and v 2 at the ends of this interval. The average acceleration is defined as follows:
a = (v 2 - v 1 ) / Ξt.
In the case of uniform motion, the speed remains constant (v 2 = v 1 ), so the value of a will be zero. In the case of uniformly accelerated displacement, the value a will be constant, therefore, it does not depend on the time interval Ξt in the formula.
For more complex cases of movement, when speed is a function of time, one should use the formula for a through the derivative, which was presented in the paragraph above.
Problem solving example
Having dealt with the question of how to find acceleration, knowing the time and speed, we will solve a simple problem. Suppose that a body moving along a certain trajectory changes its speed in accordance with this equation:
v = 3 * t 2 - t + 4.
What will be the acceleration of the body at time t = 5 seconds?
Acceleration is the first derivative of v with respect to t, we have:
a = dv / dt = 6 * t - 1.
To answer the question of the problem, you should substitute the known value of time in the resulting equation: a = 29 m / s 2 .