A dragster starts from rest and accelerates down the track. Each tire has a radius of 0.360 m and rolls without slipping. At a distance of 360 m, the angular speed of the wheels is 292 rad/s.

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(d) Determine the linear speed v of the dragster.
Number Unit
v = m/s


(e) What is the algebraic expression for the magnitude of the angular acceleration of the dragster's wheels? Express your answer in terms of the dragster's initial and final linear speeds, v0 and v, the distance x it travels, and the radius r of a wheel. (Answer using v_0 to be the initial linear speed, v to be the final linear speed, x to be the distance it travels, and and r to be the radius of the wheel).
=

(f) Determine the magnitude of the angular acceleration of the dragster's wheels.
Number Unit
= rad/s^2

To determine the linear speed v of the dragster, we can use the relationship between linear speed and angular speed. The linear speed v is equal to the product of the angular speed ω and the radius r of the wheels.

The formula for linear speed is:
v = ω * r

Given that the angular speed of the wheels is 292 rad/s and the radius of each wheel is 0.360 m, we can substitute these values into the formula to find the linear speed.

v = 292 rad/s * 0.360 m
v = 105.12 m/s

Therefore, the linear speed of the dragster is 105.12 m/s.

To find the algebraic expression for the magnitude of the angular acceleration of the dragster's wheels, we can use kinematic equations.

Let's assume the initial linear speed of the dragster is v_0, the final linear speed is v, the distance it travels is x, and the radius of the wheel is r.

The average angular speed, ω_avg, can be calculated using the equation:
ω_avg = (v - v_0) / x

The average angular speed is equal to the change in angular speed divided by the change in time. In this case, the average angular speed is equal to the difference between the final and initial angular speeds divided by the distance traveled.

Then, we can find the time it takes for the dragster to travel the distance x using the equation:
t = x / v

Finally, we can calculate the angular acceleration, α, using the equation:
α = (ω - ω_0) / t

Substituting the values into the equation, we get:
α = ((v - v_0) / x - ω_0) / (x / v)

Simplifying further, we have:
α = (v - v_0 - ω_0 * x / v) / x

Therefore, the algebraic expression for the magnitude of the angular acceleration of the dragster's wheels is (v - v_0 - ω_0 * x / v) / x.

To determine the magnitude of the angular acceleration of the dragster's wheels, we need the initial linear speed v_0, the final linear speed v, the distance x it travels, and the radius r.

Since we don't have the values for v_0 and v, we cannot determine the magnitude of the angular acceleration.

angular speed=tangential speed/radius

solve for tangential speed.

b)assuming the acceleration was constant, then

angular accleration=(wf-wo)/time=
=(Vf-vo)/(r*time)

but time= distance(avg velocity)
=distance(wf+wo)/2 * radius

put that in for time, and you have it.
angular acc= (Vf-Vo)/(r*distance*(wf+wo)2radius)

angacceleration= 1/2*(vf^2-Vo^2)/r^2 * 1/distance

a bit more can come from this...

remember the formula
vf^2 =vo^2 + 2*a*d ?
That is a standard formula you should have memorized.

Its angular form is
Wf^2=Wo^2+2 *angacceleration*distance
Memorize that.