How do you find acceleration with distance and time?

Answer 1

If the speed is zero at the beginning of the given time ... the object accelerates

from rest ... then

Distance (here comes the formula you need to keep for later) = 1/2 a T2

Multiply each side of the equation by 2 :

2 D = a T2

Divide each side by T2 :

2D/T2 = a

Acceleration = 2 x Distance/Time2

And that's the answer to your question "How . . . ".

If you ran into this problem on a test and you didn't know that formula up there

in the third line, you'd immediately run out of steam and your palms would begin

to sweat fiercely.

Here's where that formula comes from. If you can get a grip on yourself and

think clearly, here's how to build it whenever you need it:

-- You know the Distance the object moved and the Time it took, and you know

that it started from rest and accelerated uniformly.

-- "Acceleration" means how much speed it picks up every second. If it starts

from zero, then its speed at the end of 'T' is [ a T ].

-- The object's average speed during that time is distance/time . . . that's the

definition of speed.

-- The "average" means 1/2 (beginning speed + ending speed). But the

beginning speed was zero, so the average = 1/2 (ending speed).

-- Three steps ago: ending speed = a T

-- Two steps ago: Average speed = distance/time

-- One step ago: Average speed = 1/2 (ending speed) = 1/2 (a T)

-- You have two expressions for the average speed, so the expressions are equal:

Distance/time = 1/2 (a T)

Multiply both sides by the time:

Distance = 1/2 a T2

And that's the formula up in the third line. The solution for the acceleration

continues under it.