Question

A car has uniformly accelerated from rest to a speed of 25m/s after traveling 75m. What is its acceleration in m/s^2

Answer 1

So there is two truths given. After an amount of time Ttotal (lets call it ‘t’):

The car’s speed is 25m/s

The distance travelled is 75m

Then we have the formulas for speed and distance:

v = a x t -> 25 = a x t

s = 0.5 x a x t^2 -> 75 = 0.5 x a x t^2

Now, we know that both acceleration and time equal for both truths. So we can say:

t = 25 / a

t^2 = 75 / (0.5 x a) = 150 / a

Since we don’t want to use square root at 2) we go squared for 1):

t^2 = (25 / a) ^2 = 625 / a^2

t^2 = 150 / a

Since t has the same value for both truths we can say:

625 / a^2 = 150 / a

Thus multiply both sides with a^2:

625 = 150 x a, so a = 625 / 150 = 4.17

We can now calculate t as well t = 25 * 150 / 625 = 6