Newtons Laws of Motion

What is the formula for calculating acceleration?

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Answered 2015-06-07 02:59:06


There are a few. The most famous is a = F/m, where F is the net force applied to a mass, m.

Acceleration is also the change in velocity, (Delta-V), divided by the change in time, (Delta-t). So, a =Δv/Δt.

For example, if an object's velocity changes from 10 meters per second to 20 meters per second in five seconds, its acceleration is (20-10)/5 = 2 meters per second per second, or 2 meters per second squared (m/s2).

For circular motion, centripetal acceleration is v2/r, where v is the linear velocity of the rotating object and r is the radius of its circular path.

Equations in a nutshell

Constant Accelerationa = Δv/Δt = (vfinal - vinitial) / (tfinal - tinitial)

a = (v2-u2)/2s

a = 2(s - ut)/t2


a=acceleration (m/s2)

v=final velocity (m/s)

u=initial velocity (m/s)

t=time (s)

s=distance (m).



a=acceleration (m/s2)

v=final velocity (m/s)

vo=initial velocity (m/s)

t=time (s).

Newton's Second Law

F = ma, thus, a = F/m

Centripetal Acceleration

ac = v2/r

Warning: Calculus Speak:

Acceleration is the second derivative of position with respect to time: d2x / dt2, which makes it the first derivative of velocity: dv / dt. Therefore, the acceleration is the slope of the curve on the velocity-versus-time graph.


a = dv / dt = d2x / dt2

Acceleration is a quaternion with real and vector parts:

a= (V^2/R - cDel.v)) + (dcv/dR + cDelxv + V^2/R r)

a= (V^2/R - cV/R cos(v)) + (dv/dt + cv/R sin(v) + V^2/R r)

where R=ct and dR=cdt.

cv/Rcos(v) is the Centrifugal Acceleration a part of the real accelerations in the first parenthesis. The second parenthesis contains the vector accelerations.

Acceleration = F/m, where F is the net force applied to a mass, m.


acceleration in terms of velocity.

a = v - u/t Delta Velocity divided by Time.

A = ΔV ÷ T Acceleration is worked out by (final speed - initial speed)/ time taken for change in speed a = v2-v1/ t2-t1 Strictly you should say velocity ie the speed in a certain direction. Youalso have the formula f=ma which tells you that the force needed to get something moving will be the mass of the object multiplied by the accelertion you want to achieve; so from this formula if you know force and mass you can work out acceleration. The formula for acceleration is: Vf-(Vi)/t ie. change in velocity per unit time. Instantaneous acceleration in its differential form is d2x/dt2 where x is a function of time t.

Acceleration is the time rate of change of velocity.

That is, acceleration =dv/dt (v - velocity ; t - time)

Or simply acceleration = change in velocity / time

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