A car accelerates from 5 m/s to 25 m/s in 100 m.What is the car's average acceleration?

Sure, to find the average acceleration, we can use the formula:

a = (v_f - v_i) / t

where: a is the acceleration, v_f is the final velocity, v_i is the initial velocity, and t is the time.

However, in this case, we don't have the time. But we do have the distance. So we can use another formula to find the time first:

d = v_i * t + 0.5 * a * t^2

where: d is the distance.

We know that d = 100 m, v_i = 5 m/s, and v_f = 25 m/s. We can rearrange the formula to solve for t:

t = (d - 0.5 * a * t^2) / v_i

But since we don't have a, we can't solve for t directly. So we need to use another formula that relates v_f, v_i, a, and d:

v_f^2 = v_i^2 + 2 * a * d

We can rearrange this formula to solve for a:

a = (v_f^2 - v_i^2) / (2 * d)

Substituting the known values:

a = ((25 m/s)^2 - (5 m/s)^2) / (2 * 100 m) a = (625 m^2/s^2 - 25 m^2/s^2) / 200 m a = 600 m^2/s^2 / 200 m a = 3 m/s^2

So the car's average acceleration is 3 m/s^2.