Question

A race car starting from rest accelerates uniformly at a rate of 3.90 m/s^2 what is the cars speed after it has traveled 200 m.

Answer 1

Hello!

A race car starting from rest accelerates uniformly at a rate of 3.90 m/s² what is the cars speed after it has traveled 200 m.

We have the following data:

Vf (final velocity) = ? (in m/s)

Vi (initial velocity) = 0 m/s (accelerated from rest)

d (displacement) = 200 m

a (acceleration) = 3.90 m/s²

Since we do not need to know the time elapsed during the movement, we apply the data of the question to the Equation of Torricelli, let us see:

$V_f^2 = V_i^2 + 2*a*d$

$V_f^2 = 0^2 + 2*3.90*200$

$V_f^2 = 0 + 1560$

$V_f^2 = 1560$

$V_f = \sqrt{1560}$

$\boxed{\boxed{V_f \approx 39.5\:m/s}}\:\:\:\:\:\:\bf\blue{\checkmark}\bf\green{\checkmark}\bf\red{\checkmark}$

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Answer 2

The formula for accelerational displacement is at^2/2, so we know that 3.9t^2/2 = 200, or 3.9t^2 = 400. t = $\sqrt{400/3.9} \approx 10.12739367$, at = v, so $3.9 * 10.12739367 \approx 39.5 m/s$