To calculate the initial velocity (u) given the time (t), distance (d), and acceleration (a), you can use the following equation of motion:
d = ut + (1/2)at^2
In this equation, u represents the initial velocity, a represents acceleration, t represents time, and d represents distance.
To solve for u, we need to rearrange the equation. Let's go step by step:
Start with the equation: d = ut + (1/2)at^2
Move the term involving time to the left side by subtracting ut from both sides: d - ut = (1/2)at^2
Factor out the common term 't' on the left side: t(d - u) = (1/2)at^2
Divide both sides by t: d - u = (1/2)at
Solve for u by isolating it on one side: -u = (1/2)at - d
Multiply both sides by -1 to get u on the positive side: u = d - (1/2)at
Now you have the equation to calculate the initial velocity (u) when given the time (t), distance (d), and acceleration (a). Simply plug in the known values for t, d, and a to find the result.