When an object moves with constant (uniform) acceleration, its velocities, acceleration and distance are linked by one equation: (final velocity)2 − (initial velocity)2 = 2 × acceleration × distance, or v2 − u2 = 2ax. Here v and u are in m/s, a is in m/s2 and x is the distance in metres. It can be written as v2 = u2 + 2ax.
A car starts from rest, so u is zero, and it accelerates at 2 m/s2 over 25 m. Then v2 = 2 × 2 × 25 = 100. Take the square root to get v = 10 m/s. Always remember this last step, because the equation gives v2, not v.
The equation also finds stopping distances. A car travelling at 20 m/s brakes with a deceleration of 5 m/s2. When a vehicle stops, its final velocity is zero. The acceleration is entered as a negative number, −5 m/s2, so 0 − 400 = 2 × (−5) × x. This gives −400 = −10x, so the stopping distance is x = 40 m.