# Answer to Question #14439 in Mechanics | Relativity for sana

Question #14439

2 cars off to raise with velocity 2m/s & 4m/s travel in straight line with uniform acceleration 2m/s*s & 1m/s*s . what is the length covered if reach in same time?

Expert's answer

Let the length covered is L and the time of race is t.

For the first car: S1

= V10 * t + a1 * t^2 / 2.

For the second car: S2 = V20 * t + a2 * t^2 /

2.

S1 = S2 = L, so:

2 * t + 2 * t^2 / 2 = 4 * t + 1 * t^2 / 2

t^2 - 4 *

t = 0

t * (t - 4) = 0

t = {0, 4}.

At finish line t = 4

s.

Calculating L = 2 * 4 + 2 * 4^2 / 2 = 8 + 16 = 24 m.

For the first car: S1

= V10 * t + a1 * t^2 / 2.

For the second car: S2 = V20 * t + a2 * t^2 /

2.

S1 = S2 = L, so:

2 * t + 2 * t^2 / 2 = 4 * t + 1 * t^2 / 2

t^2 - 4 *

t = 0

t * (t - 4) = 0

t = {0, 4}.

At finish line t = 4

s.

Calculating L = 2 * 4 + 2 * 4^2 / 2 = 8 + 16 = 24 m.

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