A drag racer, starting from rest, speeds up for 402 m with an acceleration of +17 m/s^2. A parachute then opens, slowing the car down with an acceleration of -6.10 m/s^2. How fast us the racer moving 3.50*10^2 m after the parachute opens?
fortnite epic
Use 1 of your kinematic equations twice. vfinal^2 = vinitial^2 + 2ad.
First you want to find the speed of the drag racer right when the parachute opens.
vfinal^2 = vinitial^2 + 2ad.
Substitute 0 for vinitial^2 and take the square root of 2(17)(402).
That becomes your initial velocity for when the parachute opens. Now you have to find the final velocity so sub what you get in for vfinal as vinitial^2 in
vfinal^2 = vinitial^2 + 2ad
vfinal^2 = vinitial^2 + 2(-6.10)(3.50x10^2).
96.94
To find the speed of the racer 350 m after the parachute opens, we need to break down the problem into two parts: the first part with acceleration and the second part with deceleration.
Let's start with the first part of the problem.
Given:
Initial velocity (u) = 0 m/s
Acceleration (a) = +17 m/s^2
Distance traveled (s1) = 402 m
We can use the kinematic equation to find the final velocity (v) in this part of the motion:
v^2 = u^2 + 2as1
Substituting the given values into the equation:
v^2 = 0^2 + 2 * 17 * 402
v^2 = 0 + 13704
v^2 = 13704
Taking the square root of both sides to solve for v:
v = sqrt(13704)
v ≈ 117 m/s
So, after the acceleration phase, the racer's speed is approximately 117 m/s.
Now, let's move on to the second part of the problem.
Given:
Acceleration (a) = -6.10 m/s^2
Distance traveled (s2) = 350 m
Using the kinematic equation again, we can find the final velocity (v) in this part of the motion:
v^2 = u^2 + 2as2
Since we already know the final velocity after the first part of the motion, we can use it as the initial velocity for this part:
u = 117 m/s
Substituting the given values into the equation:
v^2 = 117^2 + 2 * (-6.10) * 350
v^2 = 13689 + (-4270)
v^2 = 9419
Taking the square root of both sides to solve for v:
v = sqrt(9419)
v ≈ 97 m/s
Therefore, the racer's speed approximately 350 m after the parachute opens is 97 m/s.